John R. Howell University of Texas at Austin
SECTION A
SECTION B
SECTION C
Differential area to differential area
Differential area to finite area
Finite area to finite area
I. Differential element to....
I. Planes and rectangles to....
II. Differential strip to....
II. Disk to....
III. Differential ring to....
III. Cylinder to....
IV. Differential sphere to....
IV. Cone to....
V. Sphere to....
VI. Hemisphere to....
VII. Other
1. Two elemental areas in arbitrary configuration.
2. Two elemental areas lying on parallel lines.
3. Elemental area of any length z to infinitely long parallel strip of differential width; plane containing element does not intersect strip.
4. Corner element on end of square channel to sectional element on channel wall.
5. Plane element to a differential coaxial ring parallel to the element.
6. Plane element on and normal to axis to inside of coaxial differential circular ring.
6a. Bounding element on wall of tapered duct to element further along duct.
7. Element on interior surface of right circular cylinder to coaxial differential ring in cylinder base.
8. Element on interior surface of right circular cone to coaxial differential ring in cone base.
9. Differential element on interior of hemisphere to a coaxial differential ring element on the base.
10. Parallel differential strip elements in intersecting planes.
11. Two elemental strip elements lying on parallel lines.
12. Infinitely long differential bounding strip to opposed parallel strip.
13. Strip of finite length and of differential width, to differential strip of same length on parallel generating line.
14. Square strip element to opposed square strip element.
15. 1x2 rectangular strip element to opposed 1x2 strip element.
16. Differential ring element to opposed ring element on coaxial disk.
17. Differential ring element on circular disk to opposed coaxial ring element on coaxial disk separated by coaxial cylinder.
18. Circumferential ring element on interior of right circular cylinder to coaxial ring element on base.
19. Ring element on exterior of tube to coaxial annular element on circular fin.
20. Two ring elements on the interior of a right circular cylinder.
21. Differential ring on surface of right circular cylinder to differential ring on parallel cylinder of the same diameter.
22. Differential ring on surface of right circular cylinder to differential ring on parallel cylinder of the same diameter. Cylinders are connected through axes by thin parallel plate.
23. Ring element on interior of right circular cylinder to ring element on interior of coaxial right circular cone.
24. Coaxial ring element to second coaxial ring element on the interior of a cone.
25. Coaxial ring element on interior of right circular cone to coaxial ring element on the interior of a butted second cone.
26. Differential ring element on the surface of a sphere to differential ring element on interior of coaxial cylinder.
27. Differential ring element on the surface of a sphere to a differential ring element in the base of a coaxial cylinder.
28. Differential ring element on base of cylinder to ring element on interior of cylinder with blockage by coaxial sphere within cylinder.
29. Differential or finite areas on the inside of a spherical cavity.
1. Differential element of any length to semi-infinite plane. Plane containing element and receiving semi-infinite plane intersect at angle Φ at edge of semiinfinite plane.
2. Differential planar element touching any convex one-, two-, or three-dimensional surface at tangent angle λ.
3. Differential planar element to finite parallel rectangle. Normal to element passes through corner of rectangle.
3a-d. Differential planar element to finite parallel rectangle. Normal to element passes through center of rectangle. Rectangle is partially shaded by rectangle in parallel plane.
3e-3h. Differential planar element to finite parallel rectangle. Normal to element passes through center of rectangle. Rectangle is partially shaded by circular disk in parallel plane.
4. Differential planar element to rectangle in plane 90° to plane of element and perpendicular to corner of plane.
5. From differential element tilted at arbitrary angle to a finite rectangle.
6. Planar element to rectangle with right triangle added. Vertex of added triangle at end of rectangle nearest element.
7. Planar element to rectangle with right triangle added. Vertex of added triangle at end of rectangle farthest from element.
8. Differential planar element to plane rectangle. Planes containing dA1 and A2 intersect at angle 0 < Φ < π . Element dA1 lies on normal to line of intersection between planes with origin at one corner of rectangle.
9. Planar element to right triangle in plane parallel to plane containing element. Normal to element passes through vertex of triangle.
10. Planar element to isosceles triangle in plane parallel to plane containing element. Normal to element passes through vertex of triangle.
11. Planar element dA1 to regular n-sided polygon A2 lying in parallel plane. Normal to element passes through center of polygon.
11a. Bounding element on wall of tapered duct to end plane of duct.
12. Planar element dA1 to circular disk A2 in parallel plane. Normal to element passes through center of disk.
13. Differential tilted planar element dA1 to disk A2. Element lies on normal to disk passing through disk center.
14. Planar element dA1 to a circular disk A2 in a parallel plane. Element is offset from normal to disk center by distance a.
15. Planar element dA1 to a circular disk A2 in a perpendicular plane.
16. Planar element dA1 to circular disk A2. Element is rotated at arbitrary angle q in x-z plane.
17. From differential element at coordinate system origin tilted at arbitrary angle to a disk bisected by the y-z plane.
18. Planar element to elliptical plate in plane parallel to element. Normal to element passes through center of plate.
18a. Tilted planar element to elliptical plate
19. Differential planar element dA1 to segment A2 of disk in parallel plane. Element lies on normal to disk passing through disk center.
20. Differential element to parallel disk segment.
21. Plane element to sector of circular disk parallel to element.
21a. Plane element to coaxial circular disk. Disk is partially shaded by disk in parallel plane.
21b-f . Plane element to coaxial circular disk. Disk is partially shaded by rectangle in parallel plane.
22. Differential element or ring on disk 1 to coaxial parallel disk 2.
23. Differential sector on disk 1 to coaxial parallel disk 2.
24. Plane element to ring sector on circular disk parallel to element.
25. Plane element to ring area in plane perpendicular to element.
26. Element on coaxial annular disk to second annular disk separated by coaxial cylinder.
27. Plane element to annular disk with conical blockage of view.
28. Plane element to interior of coaxial right circular cylinder.
29. Planar or coaxial ring element in plane perpendicular to cylinder axis to right circular cylinder of finite length.
29a. Planar element on interior cylinder surface to finite segment.
29b. Planar element on interior cylinder surface to finite wall area of cylinder length.
29c. Planar element d1 on interior cylinder surface to finite segment A2 on cylinder end.
29d. Planar element d1 on interior cylinder surface to finite segment A2 on cylinder end.
30. Differential element on annulus between coaxial cylinders to interior of outer cylinder.
31. Plane element to right circular cylinder of finite length and radius, normal to element passes through one end of cylinder and is perpendicular to cylinder axis.
32. Element on plane to exterior of right circular cylinder of finite length. Plane does not intersect cylinder.
33. Front face of plane vertical element to circular cylinder tilted toward the element.
34. Vertical or horizontal element to base of a tilted cylinder.
34a. Vertical or horizontal element to side of a tilted cylinder; element in plane of cylinder base.
35. Plane element on a ring to an inverted cone; ring and cone have the same axis and plane of ring does not intersect cone.
36. Plane element on a ring to an inverted cone; ring and cone have the same axis and plane of ring intersects cone.
37. Plane element to exterior of right circular truncated cone; element and cone base are in the same plane.
38. Differential element tilted in y-z plane to inverted cone.
39. Plane element to sphere; normal to center of element passes through center of sphere.
40. Plane element to sphere; tangent to element passes through center of sphere.
41. Differential planar element to sphere; element plane does not intersect sphere.
42. Differential planar element to sphere; element plane intersects sphere.
43. Arbitrarily oriented differential planar element to a sphere
43a. Vertically oriented differential planar element to a partially shadowed ground level or rising sphere.
44. Area element to sphere; element lies in plane perpendicular to sphere axis.
45. Differential element on non-coaxial disk ring to sphere; plane of element does not intersect sphere.
46. Plane element to sphere.
47. Differential element parallel to sphere axis to sphere.
47a. Tilted differential element to spheroid
48. From differential element at coordinate system origin tilted at arbitrrary angle to a hemisphere with base in the x-z plane and a center at height z=h.
49. Differential element on plane to standing standard person facing plane.
50. Differential element on vertical plane to seated standard person facing plane.
51. Element on longitudinal strip inside cylinder to inside cylinder surface.
52. Element on longitudinal strip on inside of right circular cylinder to base of cylinder.
53. Differential element on surface of right circular cylinder to disk on base of cylinder, r2 <rr.
54. Element on interior of coaxial right circular cylinder sitting atop a second cylinder of larger radius to base of lower cylinder.
55. Element at end of outer cylinder to inside of outer coaxial cylinder.
56. Element on strip inside cylinder to entire interior surface of outer concentric right circular cylinder.
57. Element on parallel strip on interior of outer cylinder to exterior of concentric smaller right circular cylinder.
58. Differential element on interior of right circular cylinder of finite length to annular end enclosing space between coaxial cylinders.
59. Element on strip on exterior surface of inner coaxial right circular cylinder to inner surface of outer cylinder.
60. Element on strip on exterior surface of inner coaxial cylinder to annular end enclosing space between cylinders.
61. Element on surface of cylinder at longitude a to sphere; axis of sphere bisects and is normal to cylinder axis.
62. Element on internal surface of right circular cone to base of cone.
63. Element on interior of right circular cone to coaxial disk on base.
64. Any differential area on the interior of a hemisphere to the entire base.
65. Element on interior of hemisphere to section from base to height l.
66. Differential element or ring on interior of hemisphere to a coaxial disk in base.
67. Element or coaxial ring on surface of sphere to sphere.
68. Differential planar element on ceiling, floor or any wall to cow.
69. Differential area on the inside of a spherical cavity to finite area on interior of sphere.
70. Infinite strip to parallel infinite plane of finite width. Plane and plane containing strip intersect at arbitrary angle.
71. Differential element of any length to surface generated by a line of infinite length parallel to the plane of the element, and moved parallel to itself. Plane of element does not intersect surface.
72. Infinite differential bounding strip elements to infinitely long opposed strip.
73. Infinitely long strip of differential width to parallel semi-cylinder. Strip element and cylinder axis are in the same plane.
74. Infinitely long strip element to infinitely long parallel cylinder.
75. Strip element to rectangle in plane parallel to strip; strip is opposite one edge of rectangle.
76. Strip element to rectangle in plane 90o to plane of strip.
77. Strip of finite length to opposed rectangle of infinite width. Plane containing strip intersects rectangle at angle Φ .
78. A strip element to a rectangular plane intersecting at an angle Φ .
79. Strip element to parallel opposed right circular cylinder of same length as strip.
80. Strip element on plane to exterior of right circular cylinder of finite length. Strip and cylinder are parallel, and of equal length. Plane does not intersect cylinder.
81. Vertical differential strip on plane contained in cylinder with axis parallel to strip. Strip and cylinder of equal length. Factor from strip to entire inner surface of cylinder.
82. Square strip element to opposed square.
83. 1 x 2 rectangular strip to 1 x 2 opposed rectangle.
84. Element of any length on exterior of cylinder to plane of infinite length and width.
85. Infinitely long differential strip element on tube to fin.
86. Longitudinal strip element on inside of right circular cylinder to entire inside cylinder surface.
87. Longitudinal strip element on inside of right circular cylinder to base of cylinder.
88. Strip on interior of outer cylinder to entire interior of outer right circular coaxial cylinder.
89. Strip on interior of outer cylinder to exterior of inner opposed right circular coaxial cylinder.
90. Strip on interior of outer right circular cylinder of finite length to annular end enclosing space between coaxial cylinders.
III. Ring element to....
91. Differential ring element on surface of disk to coaxial sphere.
92. Sector of differential ring element on surface of disk to coaxial sphere.
93. Ring element on interior of right circular cylinder to circular disk at end of cylinder.
94. Ring element on base of right circular cylinder to finite circumferential ring on interior of cylinder.
95. Ring element on interior of right circular cone to end of frustum on cone.
96. Ring element on interior of right circular cone to coaxial disk.
97. Conical ring element to coaxial body of revolution (cone, paraboloid, or ellipsoid).
98. Exterior of differential conical ring to coaxial sphere, Case I.
99. Exterior of differential conical ring to coaxial sphere, Case II.
100. Differential ring on surface of right circular cylinder to finite area on surface of parallel cylinder of the same diameter. End of finite area is opposite the ring.
101. Differential ring on surface of right circular cylinder to finite area on surface of parallel cylinder of the same diameter. End of finite area is opposite the ring. Axes of cylinders are connected by thin plate of width 2l.
102. Differential ring element on base of cylinder to finite ring on interior of cylinder with blockage by coaxial sphere within cylinder.
103. Differential ring on interior of hemisphere to disk on base.
104. Differential ring element on the surface of a sphere to finite ring on interior of coaxial cylinder.
105. Differential ring sector to spherical segment.
106. Spherical point source to plane rectangle. Point source lies on corner of adjacent rectangle with common side and intersecting A2 at angle ø
107. Spherical point source to sphere.
108. Element on surface of hemisphere to second hemisphere in contact.
1. Two infinitely long, directly opposed parallel plates of the same finite width. Click to open calculator >>
2. Two infinitely long parallel plates of different widths; centerlines of plates are connected by perpendicular between plates. Click to open calculator >>
2a. Two infinitely long parallel plates of different widths contained in parallel planes.
3. Two infinitely long plates of unequal widths h and w, having one common edge, and at an angle of 90o to each other. Click to open calculator >>
4. Two infinitely long plates of equal widths having a common edge and included angle a Click to open calculator >>
5. Two infinitely long plates of unequal width having a common edge with an included angle α Click to open calculator >>
5a. Two infinitely long plates of unequal width without a common edge with an included angle α.
6. Infinitely long enclosure formed by three planar or convex surfaces. Click to open calculator >>
7. Infinite plane to row of parallel cylinders, or n rows of in-line cylinders. Click to open calculator >>
8. Infinite plane to first, second, and first plus second rows of infinitely long parallel tubes of equal diameter in equilateral triangular array. Click to open calculator >>
9. Top surface of finite rectangle tilted relative to an infinite plane. Click to open calculator >>
9a. General Solutions for two arbitrary rectangles in parallel or perpendicular planes. Click to open calculator >>
9b. Simple general solutions for two arbitrary rectangles in parallel or perpendicular planes. Click to open calculator >>
10. Rectangles having a common edge and forming an arbitrary angle; one rectangle infinitely long. Click to open calculator >>
11. Identical, parallel, directly opposed rectangles. Click to open calculator >>
12. Coaxial parallel squares of different edge length. Click to open calculator >>
12a.Squares of different edge length in perpendicular planes. One corner of square 2 touches plane containing unit square 1 Click to open calculator >>
13. Rectangle to rectangle in a parallel plane; all boundaries are parallel or perpendicular to x and x boundaries. Click to open calculator >>
13a.Rectangle to coaxial disk in a parallel plane Click to open calculator >>
13b.Rectangle to torus in parallel plane.
13c.Rectangle to W-shaped tube in parallel plane.
14.Two finite rectangles of same length, having one common edge, and at an angle of 90o to each other. Click to open calculator >>
15. Rectangle to rectangle in a perpendicular plane; all boundaries are parallel or perpendicular to x and ξ boundaries. Click to open calculator >>
15a.Rectangle to disk in perpendicular plane. Disk is symmetrically centered with rectangle, and touches rectangle center Click to open calculator >>
16. Two rectangles with one common edge and included angle of Φ. Click to open calculator >>
17. Rectangle 1 to rectangle 2 in a plane intersecting the plane containing rectangle 1. All rectangle edges are parallel or perpendicular to the line of intersection of the containing planes. Click to open calculator >>
18. Finite area on interior of rectangular enclosure to second finite area. Click to open calculator >>
19. Right triangle to perpendicular rectangle with common side. Click to open calculator >>
20. Isosceles triangle to perpendicular rectangle: Base of triangle and rectangle have common edge. Click to open calculator >>
21. Right triangle with side of length one-half that of perpendicular rectangle to rectangle. Click to open calculator >>
22. Perpendicular right triangles with one equal edge. Click to open calculator >>
23. Right triangle to perpendicular right triangle with common edge; apexes at common point. Click to open calculator >>
24. Right triangle to perpendicular right triangle with common edge; apexes at opposite ends. Click to open calculator >>
25. Triangle to perpendicular rectangle. Click to open calculator >>
26. Right triangle to perpendicular right triangle of unequal size; apexes at opposite ends of shared edge. Click to open calculator >>
27. Right triangle to perpendicular right triangle of unequal size; apexes at common point. Click to open calculator >>
28. Right isosceles triangle to adjacent congruent perpendicular triangle connected along short side. Click to open calculator >>
29. Parallel directly opposed right triangles. Click to open calculator >>
30. Parallel directly opposed rectangles with triangular extensions. Click to open calculator >>
31. Floor to end wall with triangular extension. Click to open calculator >>
32. Side wall to end wall with triangular extension. Click to open calculator >>
33. Between all combinations of surfaces in a hexagonal prism. Click to open calculator >>
34. Between parallel regular polygons. Click to open calculator >>
35. One side of rectangle to one quarter of parallel cylinder of same length as rectangle; cylinder is bisected longitudinally by plane containing rectangle. Click to open calculator >>
36. Rectangle to perpendicular circular segment. Click to open calculator >>
37. Horizontal panel to adjacent vertical panel with circular segment on top. Click to open calculator >>
38. Side wall to end wall with circular segment extension. Click to open calculator >>
39. Circular disk to parallel right triangle; normal from center of circle passes through one acute vertex. Click to open calculator >>
40. Disk to parallel coaxial disk of same radius. Click to open calculator >>
41. Disk to parallel coaxial disk of unequal radius. Click to open calculator >>
42. Disk to second coaxial disk inside cone. Click to open calculator >>
43. Nonintersecting disks with intersecting axes; axes intersect between disks; and disks can be inscribed in sphere of radius r3 (i.e. r12 + h12 = r22 + h22 = r32) Click to open calculator >>
43a. Two Half disks of the same radius with a common edge forming any agnle a From 0 to pi.
43b. Enclosure bounded by two half disks of a same radius with o common edge forming any angle a from 0 to pi.
44. Nonintersecting disks with intersecting axes; axes do not intersect between disks. Disks can be inscribed in sphere of radius r3 (i.e. r12 + h12 = r22 + h22 = r32) Click to open calculator >>
45. Sector of circular disk to sector of parallel circular disk. Click to open calculator >>
46. Parallel opposed circular segments. Click to open calculator >>
47. Disk to coaxial annular ring on parallel disk. Click to open calculator >>
48. Disk to coaxial cone. Click to open calculator >>
49. Annular Disk to coaxial truncated cone; cone can be convergent (+α) or divergent (-α). Click to open calculator >>
50. Disk to a coaxial paraboloid. Click to open calculator >>
51. Disk to coaxial ellipsoid. Click to open calculator >>
52. Ring to parallel coaxial ring. Click to open calculator >>
53. Annulus to coaxial annulus of different outer radius; both annuli have inner radius of blocking coaxial cylinder. Click to open calculator >>
54. Coaxial annular rings separated by coaxial cylinder. Click to open calculator >>
55. Annular ring between two concentric cylinders to inside of outer cylinder; inner radius of ring is equal to radius of inner cylinder. Click to open calculator >>
56. Ring on annulus between coaxial cylinders to inner surface of outer cylinder. Click to open calculator >>
57. Annular ring around base of hemisphere to hemisphere. Click to open calculator >>
58. Ring around base of hemisphere to section of hemisphere. Click to open calculator >>
59. Annular ring to attached coaxial paraboloid. Click to open calculator >>
60. Annular ring to attached coaxial ellipsoid. Click to open calculator >>
61. Exterior of infinitely long cylinder to symmetrically placed infinitely long parallel rectangle. Click to open calculator >>
62. Exterior of infinitely long cylinder to unsymmetrically placed infinitely long parallel plate. Click to open calculator >>
63. Concentric cylinders of infinite length. Click to open calculator >>
64. Exterior of infinitely long cylinder to interior of concentric semicylinder. Click to open calculator >>
65. Interior of infinitely long semicylinder to itself when concentric coaxial cylinder is present. Click to open calculator >>
66. Interior of infinitely long semicylinder 1 to interior of semicylinder 2 when concentric parallel cylinder 3 is present. Click to open calculator >>
67. Infinitely long cylinder to non-concentric cylindrical enclosure. Click to open calculator >>
68. Infinitely long parallel cylinders of the same diameter. Click to open calculator >>
69. Infinite parallel cylinders of different radius. Click to open calculator >>
70. Infinitely long facing parallel semicylinders of equal radius. Click to open calculator >>
71. Infinitely long semicylinder to parallel infinitely long semicylinder of same radius. Click to open calculator >>
72. Infinitely long cylinder to other cylinders in square array of parallel cylinders of equal diameter. Click to open calculator >>
73. Infinitely long cylinder to other cylinders in equilateral triangular array of parallel cylinders of equal diameter. Click to open calculator >>
74. Finite-length cylinder to rectangle with two edges parallel to cylinder axis and of length equal to cylinder. Click to open calculator >>
75. Finite cylinder to finite rectangle of same length. Click to open calculator >>
76. Outside surface of cylinder to perpendicular right triangle; triangle is in plane of cylinder base with one vertex of triangle at center of base. Click to open calculator >>
77. Outer surface of cylinder to annular disk at end of cylinder. Click to open calculator >>
78. Inner surface of right circular cylinder to itself. Click to open calculator >>
78a. Flat spiral tape of width h rolled around imaginary cylinder of diameter d and length l. 78b. Long flat double helix. 79. Base of right circular cylinder to inside surface of cylinder. Click to open calculator >> 80. Disk in cylinder base or top to inside surface of right circular cylinder. Click to open calculator >> 81. Inside surface of right cylinder to coaxial disk of same diameter separated from base of cylinder. Click to open calculator >> 82. Interior surface of circular cylinder of radius R to disk of radius r where r < R; disk is perpendicular to axis of cylinder, and axis passes through center of disk. Click to open calculator >> 83. Annular ring on cylinder base or top to inside of right circular cylinder. Click to open calculator >> 84. Interior of right circular cylinder to finite annular ring in base. Click to open calculator >> 85. Inner surface of upper cylinder to base ring. Click to open calculator >> 86. Inside surface of right circular cylinder to inside surface of adjacent right circular cylinder of the same diameter. Click to open calculator >> 87. Finite section of right circular cylinder to separated finite section. Click to open calculator >> 88. Interior of half-cylinder to interior of opposed adjacent coaxial half-cylinder of equal length. Click to open calculator >> 89. Coaxial right circular cylinders of different radii, one atop the other, Case I. Click to open calculator >> 90. Coaxial right circular cylinders of different radii, one atop the other, Case II. Click to open calculator >> 91. Interior of finite length right circular coaxial cylinder to itself. Click to open calculator >> 92. Interior of outer right circular cylinder of finite length to exterior of coaxial inner right circular cylinder. Click to open calculator >> 93. Interior of outer right circular cylinder of finite length to annular end enclosing space between coaxial cylinders. Click to open calculator >> 94. Annular end enclosing space between coaxial right circular cylinders to opposite annular end. Click to open calculator >> 95. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder entirely within outer. Click to open calculator >> 96. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder extends beyond one end of outer. Click to open calculator >> 97. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder extends beyond both ends of outer. Click to open calculator >> 98. Outside of inner (smaller) coaxial cylinder to inside of larger cylinder; small cylinder completely outside larger. Click to open calculator >> 99. Between equal length cylindrical areas on interior of outer coaxial cylinder. Click to open calculator >> 100. Between cylindrical area on interior of shell and equal length cylindrical area on exterior of inner coaxial cylinder. Click to open calculator >> 101. Parallel opposed cylinders of unequal radius and equal finite length. Click to open calculator >> 102. Perpendicular cylinders of equal radius and equal finite length, closest separation at centers. Click to open calculator >> 103. Cylinders of equal radius and length, one cylinder rotated around line joining centers. Click to open calculator >> 104. Finite cylinders of equal radius and length. Cylinders are rotated at 90o from line connecting their ends. Click to open calculator >> 105. Cylinders of equal length and radius, rotated around line connecting ends. Click to open calculator >> 106. Cylinder of length l/2 to perpendicular cylinder of length l and same radius. Cylinder axes intersect at center of longer cylinder. Click to open calculator >> 107. Cylinder of length l/2 to cylinder of equal radius and length l rotated in plane containing cylinder axes about a line through end of longer cylinder. Click to open calculator >> 108. Cylinder of length l/2 to skewed cylinder of equal radius and length. Click to open calculator >> IV. Cone to.... 109. Interior of right circular cone to base. Click to open calculator >> 110. Interior of right circular cone to itself. Click to open calculator >> 111. Interior of frustum of right circular cone to base. Click to open calculator >> 111a Interior of Frustum of Right Circular Cone to Itself Click to open calculator >> 112. Frustum of right circular cone to entire base. Click to open calculator >> 112a. Frustum of right circular cone to base with obstruction by coaxial internal cylinder Click to open calculator >> 113. Frustum of right circular cone to disk in base of cone. Click to open calculator >> 114. Frustum of right circular cone cut by plane parallel to cone axis. Click to open calculator >> 115. Finite section of right circular cone to separated finite section. Click to open calculator >> 116. Interior of frustum of right circular cone to attached right circular cone. Click to open calculator >> 117. Interior of right circular cone to base of attached frustum. Click to open calculator >> 118. Frustum of right circular cone to coaxial attached frustum. Click to open calculator >> 119. Interior of frustum of right circular cone to base of attached coaxial frustum. Click to open calculator >> 120. Cone to coaxial body of revolution (cone, paraboloid or ellipsoid). Click to open calculator >> V. Sphere to.... 121. Sphere to rectangle perpendicular to line through sphere axis. Click to open calculator >> 122. Sphere to rectangle. Click to open calculator >> 122a. Sphere to plane rectangle. Sphere lies on corner of adjacent rectangle with common side and intersecting A2 at angle ø Click to open calculator >> 123. Sphere to scalene triangle in plane perpendicular to sphere axis with one vertex on axis; sphere does not intersect plane of triangle. Click to open calculator >> 124. Sphere to any polygon in plane that does not intersect sphere. Click to open calculator >> 125. Sphere to coaxial disk. Click to open calculator >> 126. Sphere to noncoaxial disk; plane of disk does not intersect sphere. Point o may lie inside or outside disk. Click to open calculator >> 127. Sphere to sector on coaxial disk. Click to open calculator >> 128. Sphere to segment on a coaxial disk. Click to open calculator >> 129. Sphere to top of coaxial annular ring not touching sphere. Click to open calculator >> 130. Sphere to top of coaxial annular ring touching sphere. Click to open calculator >> 131. Sphere to interior surface of coaxial right circular cylinder; sphere outside end of cylinder, and sphere radius less than cylinder radius. Click to open calculator >> 132. Sphere to interior surface of coaxial right circular cylinder; sphere within ends of cylinder. Click to open calculator >> 133. Sphere to exterior of coaxial cylinder. Click to open calculator >> 134. Large sphere to small cylinder. r>> diameter or length of cylinder. Click to open calculator >> 135. Concentric spheres. Click to open calculator >> 136. Differential or finite areas on the inside of a spherical cavity. Click to open calculator >> 137. Two spheres of unequal radius. Click to open calculator >> 138. Sphere to spherical cap. Click to open calculator >> 139. Sphere to coaxial cone. Click to open calculator >> 140. Large sphere to small hemisphere (not including circular base). Click to open calculator >> 140a. Two directly opposed spherical caps on a common axis. 140b. Spherical cap on a sphere of radius r to itself and to its base 140c. Two complementary spherical caps on the same sphere of radius r. 140d. Two spherical caps of different size in the same sphere of radius r 140e. Euclidian spherical spiral with uniform spiral band. 140f. Logarithmic spherical spiral band. 141. Sphere to coaxial paraboloid. Click to open calculator >> 142. Sphere to coaxial ellipsoid. Click to open calculator >> 143. Large sphere to small ellipsoid. Click to open calculator >> 144. Ring area on inside of sphere to coaxial ring area on inside of attached frustum. Click to open calculator >> 145. Ring area on inside of sphere to ring on interior of cylinder attached to sphere by a conical frustum. Click to open calculator >> VI. Hemisphere to.... 146. Any finite area of any shape on interior of hemisphere to entire base. Click to open calculator >> 147. Spherical cap to disk in equatorial plane. Click to open calculator >> 148. Interior finite section of hemisphere to itself. Click to open calculator >> 149. Finite section on interior of hemisphere to parallel finite section. Click to open calculator >> 150. Section of interior of hemisphere to disk on base. Click to open calculator >> 151. Finite section of interior of hemisphere to disk on base. Click to open calculator >> 152. Section of hemisphere to annular ring in base. Click to open calculator >> 153. Ring on hemispherical surface to ring on the base. Click to open calculator >> 154. Two hemispheres in contact. Click to open calculator >> VII. Other 155. Moebius strip of constant width to itself. Click to open calculator >> 155a. Spiral strip on inside of right circular cylinder to itself Click to open calculator >> 156. Seated standard person facing vertical panel. Click to open calculator >> 157. Seated standard person to side vertical rectangle. Click to open calculator >> 158. Seated standard person to rectangle on ceiling or floor. Click to open calculator >> 159. Standard standing person to rectangle on ceiling. Click to open calculator >> 160. Standing standard person to side vertical rectangle. Click to open calculator >> 161. Standing standard person to vertical facing rectangle. Click to open calculator >> 162. Pig to rectangle in various orientations. Click to open calculator >>
78b. Long flat double helix. 79. Base of right circular cylinder to inside surface of cylinder. Click to open calculator >> 80. Disk in cylinder base or top to inside surface of right circular cylinder. Click to open calculator >> 81. Inside surface of right cylinder to coaxial disk of same diameter separated from base of cylinder. Click to open calculator >> 82. Interior surface of circular cylinder of radius R to disk of radius r where r < R; disk is perpendicular to axis of cylinder, and axis passes through center of disk. Click to open calculator >> 83. Annular ring on cylinder base or top to inside of right circular cylinder. Click to open calculator >> 84. Interior of right circular cylinder to finite annular ring in base. Click to open calculator >> 85. Inner surface of upper cylinder to base ring. Click to open calculator >> 86. Inside surface of right circular cylinder to inside surface of adjacent right circular cylinder of the same diameter. Click to open calculator >> 87. Finite section of right circular cylinder to separated finite section. Click to open calculator >> 88. Interior of half-cylinder to interior of opposed adjacent coaxial half-cylinder of equal length. Click to open calculator >> 89. Coaxial right circular cylinders of different radii, one atop the other, Case I. Click to open calculator >> 90. Coaxial right circular cylinders of different radii, one atop the other, Case II. Click to open calculator >> 91. Interior of finite length right circular coaxial cylinder to itself. Click to open calculator >> 92. Interior of outer right circular cylinder of finite length to exterior of coaxial inner right circular cylinder. Click to open calculator >> 93. Interior of outer right circular cylinder of finite length to annular end enclosing space between coaxial cylinders. Click to open calculator >> 94. Annular end enclosing space between coaxial right circular cylinders to opposite annular end. Click to open calculator >> 95. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder entirely within outer. Click to open calculator >> 96. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder extends beyond one end of outer. Click to open calculator >> 97. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder extends beyond both ends of outer. Click to open calculator >> 98. Outside of inner (smaller) coaxial cylinder to inside of larger cylinder; small cylinder completely outside larger. Click to open calculator >> 99. Between equal length cylindrical areas on interior of outer coaxial cylinder. Click to open calculator >> 100. Between cylindrical area on interior of shell and equal length cylindrical area on exterior of inner coaxial cylinder. Click to open calculator >> 101. Parallel opposed cylinders of unequal radius and equal finite length. Click to open calculator >> 102. Perpendicular cylinders of equal radius and equal finite length, closest separation at centers. Click to open calculator >> 103. Cylinders of equal radius and length, one cylinder rotated around line joining centers. Click to open calculator >> 104. Finite cylinders of equal radius and length. Cylinders are rotated at 90o from line connecting their ends. Click to open calculator >> 105. Cylinders of equal length and radius, rotated around line connecting ends. Click to open calculator >> 106. Cylinder of length l/2 to perpendicular cylinder of length l and same radius. Cylinder axes intersect at center of longer cylinder. Click to open calculator >> 107. Cylinder of length l/2 to cylinder of equal radius and length l rotated in plane containing cylinder axes about a line through end of longer cylinder. Click to open calculator >> 108. Cylinder of length l/2 to skewed cylinder of equal radius and length. Click to open calculator >> IV. Cone to.... 109. Interior of right circular cone to base. Click to open calculator >> 110. Interior of right circular cone to itself. Click to open calculator >> 111. Interior of frustum of right circular cone to base. Click to open calculator >> 111a Interior of Frustum of Right Circular Cone to Itself Click to open calculator >> 112. Frustum of right circular cone to entire base. Click to open calculator >> 112a. Frustum of right circular cone to base with obstruction by coaxial internal cylinder Click to open calculator >> 113. Frustum of right circular cone to disk in base of cone. Click to open calculator >> 114. Frustum of right circular cone cut by plane parallel to cone axis. Click to open calculator >> 115. Finite section of right circular cone to separated finite section. Click to open calculator >> 116. Interior of frustum of right circular cone to attached right circular cone. Click to open calculator >> 117. Interior of right circular cone to base of attached frustum. Click to open calculator >> 118. Frustum of right circular cone to coaxial attached frustum. Click to open calculator >> 119. Interior of frustum of right circular cone to base of attached coaxial frustum. Click to open calculator >> 120. Cone to coaxial body of revolution (cone, paraboloid or ellipsoid). Click to open calculator >> V. Sphere to.... 121. Sphere to rectangle perpendicular to line through sphere axis. Click to open calculator >> 122. Sphere to rectangle. Click to open calculator >> 122a. Sphere to plane rectangle. Sphere lies on corner of adjacent rectangle with common side and intersecting A2 at angle ø Click to open calculator >> 123. Sphere to scalene triangle in plane perpendicular to sphere axis with one vertex on axis; sphere does not intersect plane of triangle. Click to open calculator >> 124. Sphere to any polygon in plane that does not intersect sphere. Click to open calculator >> 125. Sphere to coaxial disk. Click to open calculator >> 126. Sphere to noncoaxial disk; plane of disk does not intersect sphere. Point o may lie inside or outside disk. Click to open calculator >> 127. Sphere to sector on coaxial disk. Click to open calculator >> 128. Sphere to segment on a coaxial disk. Click to open calculator >> 129. Sphere to top of coaxial annular ring not touching sphere. Click to open calculator >> 130. Sphere to top of coaxial annular ring touching sphere. Click to open calculator >> 131. Sphere to interior surface of coaxial right circular cylinder; sphere outside end of cylinder, and sphere radius less than cylinder radius. Click to open calculator >> 132. Sphere to interior surface of coaxial right circular cylinder; sphere within ends of cylinder. Click to open calculator >> 133. Sphere to exterior of coaxial cylinder. Click to open calculator >> 134. Large sphere to small cylinder. r>> diameter or length of cylinder. Click to open calculator >> 135. Concentric spheres. Click to open calculator >> 136. Differential or finite areas on the inside of a spherical cavity. Click to open calculator >> 137. Two spheres of unequal radius. Click to open calculator >> 138. Sphere to spherical cap. Click to open calculator >> 139. Sphere to coaxial cone. Click to open calculator >> 140. Large sphere to small hemisphere (not including circular base). Click to open calculator >> 140a. Two directly opposed spherical caps on a common axis. 140b. Spherical cap on a sphere of radius r to itself and to its base 140c. Two complementary spherical caps on the same sphere of radius r. 140d. Two spherical caps of different size in the same sphere of radius r 140e. Euclidian spherical spiral with uniform spiral band. 140f. Logarithmic spherical spiral band. 141. Sphere to coaxial paraboloid. Click to open calculator >> 142. Sphere to coaxial ellipsoid. Click to open calculator >> 143. Large sphere to small ellipsoid. Click to open calculator >> 144. Ring area on inside of sphere to coaxial ring area on inside of attached frustum. Click to open calculator >> 145. Ring area on inside of sphere to ring on interior of cylinder attached to sphere by a conical frustum. Click to open calculator >> VI. Hemisphere to.... 146. Any finite area of any shape on interior of hemisphere to entire base. Click to open calculator >> 147. Spherical cap to disk in equatorial plane. Click to open calculator >> 148. Interior finite section of hemisphere to itself. Click to open calculator >> 149. Finite section on interior of hemisphere to parallel finite section. Click to open calculator >> 150. Section of interior of hemisphere to disk on base. Click to open calculator >> 151. Finite section of interior of hemisphere to disk on base. Click to open calculator >> 152. Section of hemisphere to annular ring in base. Click to open calculator >> 153. Ring on hemispherical surface to ring on the base. Click to open calculator >> 154. Two hemispheres in contact. Click to open calculator >> VII. Other 155. Moebius strip of constant width to itself. Click to open calculator >> 155a. Spiral strip on inside of right circular cylinder to itself Click to open calculator >> 156. Seated standard person facing vertical panel. Click to open calculator >> 157. Seated standard person to side vertical rectangle. Click to open calculator >> 158. Seated standard person to rectangle on ceiling or floor. Click to open calculator >> 159. Standard standing person to rectangle on ceiling. Click to open calculator >> 160. Standing standard person to side vertical rectangle. Click to open calculator >> 161. Standing standard person to vertical facing rectangle. Click to open calculator >> 162. Pig to rectangle in various orientations. Click to open calculator >>
79. Base of right circular cylinder to inside surface of cylinder. Click to open calculator >>
80. Disk in cylinder base or top to inside surface of right circular cylinder. Click to open calculator >>
81. Inside surface of right cylinder to coaxial disk of same diameter separated from base of cylinder. Click to open calculator >>
82. Interior surface of circular cylinder of radius R to disk of radius r where r < R; disk is perpendicular to axis of cylinder, and axis passes through center of disk. Click to open calculator >>
83. Annular ring on cylinder base or top to inside of right circular cylinder. Click to open calculator >>
84. Interior of right circular cylinder to finite annular ring in base. Click to open calculator >>
85. Inner surface of upper cylinder to base ring. Click to open calculator >>
86. Inside surface of right circular cylinder to inside surface of adjacent right circular cylinder of the same diameter. Click to open calculator >>
87. Finite section of right circular cylinder to separated finite section. Click to open calculator >>
88. Interior of half-cylinder to interior of opposed adjacent coaxial half-cylinder of equal length. Click to open calculator >>
89. Coaxial right circular cylinders of different radii, one atop the other, Case I. Click to open calculator >>
90. Coaxial right circular cylinders of different radii, one atop the other, Case II. Click to open calculator >>
91. Interior of finite length right circular coaxial cylinder to itself. Click to open calculator >>
92. Interior of outer right circular cylinder of finite length to exterior of coaxial inner right circular cylinder. Click to open calculator >>
93. Interior of outer right circular cylinder of finite length to annular end enclosing space between coaxial cylinders. Click to open calculator >>
94. Annular end enclosing space between coaxial right circular cylinders to opposite annular end. Click to open calculator >>
95. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder entirely within outer. Click to open calculator >>
96. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder extends beyond one end of outer. Click to open calculator >>
97. Inner coaxial cylinder to outer coaxial cylinder; inner cylinder extends beyond both ends of outer. Click to open calculator >>
98. Outside of inner (smaller) coaxial cylinder to inside of larger cylinder; small cylinder completely outside larger. Click to open calculator >>
99. Between equal length cylindrical areas on interior of outer coaxial cylinder. Click to open calculator >>
100. Between cylindrical area on interior of shell and equal length cylindrical area on exterior of inner coaxial cylinder. Click to open calculator >>
101. Parallel opposed cylinders of unequal radius and equal finite length. Click to open calculator >>
102. Perpendicular cylinders of equal radius and equal finite length, closest separation at centers. Click to open calculator >>
103. Cylinders of equal radius and length, one cylinder rotated around line joining centers. Click to open calculator >>
104. Finite cylinders of equal radius and length. Cylinders are rotated at 90o from line connecting their ends. Click to open calculator >>
105. Cylinders of equal length and radius, rotated around line connecting ends. Click to open calculator >>
106. Cylinder of length l/2 to perpendicular cylinder of length l and same radius. Cylinder axes intersect at center of longer cylinder. Click to open calculator >>
107. Cylinder of length l/2 to cylinder of equal radius and length l rotated in plane containing cylinder axes about a line through end of longer cylinder. Click to open calculator >>
108. Cylinder of length l/2 to skewed cylinder of equal radius and length. Click to open calculator >>
109. Interior of right circular cone to base. Click to open calculator >>
110. Interior of right circular cone to itself. Click to open calculator >>
111. Interior of frustum of right circular cone to base. Click to open calculator >>
111a Interior of Frustum of Right Circular Cone to Itself Click to open calculator >>
112. Frustum of right circular cone to entire base. Click to open calculator >>
112a. Frustum of right circular cone to base with obstruction by coaxial internal cylinder Click to open calculator >>
113. Frustum of right circular cone to disk in base of cone. Click to open calculator >>
114. Frustum of right circular cone cut by plane parallel to cone axis. Click to open calculator >>
115. Finite section of right circular cone to separated finite section. Click to open calculator >>
116. Interior of frustum of right circular cone to attached right circular cone. Click to open calculator >>
117. Interior of right circular cone to base of attached frustum. Click to open calculator >>
118. Frustum of right circular cone to coaxial attached frustum. Click to open calculator >>
119. Interior of frustum of right circular cone to base of attached coaxial frustum. Click to open calculator >>
120. Cone to coaxial body of revolution (cone, paraboloid or ellipsoid). Click to open calculator >>
121. Sphere to rectangle perpendicular to line through sphere axis. Click to open calculator >>
122. Sphere to rectangle. Click to open calculator >>
122a. Sphere to plane rectangle. Sphere lies on corner of adjacent rectangle with common side and intersecting A2 at angle ø Click to open calculator >>
123. Sphere to scalene triangle in plane perpendicular to sphere axis with one vertex on axis; sphere does not intersect plane of triangle. Click to open calculator >>
124. Sphere to any polygon in plane that does not intersect sphere. Click to open calculator >>
125. Sphere to coaxial disk. Click to open calculator >>
126. Sphere to noncoaxial disk; plane of disk does not intersect sphere. Point o may lie inside or outside disk. Click to open calculator >>
127. Sphere to sector on coaxial disk. Click to open calculator >>
128. Sphere to segment on a coaxial disk. Click to open calculator >>
129. Sphere to top of coaxial annular ring not touching sphere. Click to open calculator >>
130. Sphere to top of coaxial annular ring touching sphere. Click to open calculator >>
131. Sphere to interior surface of coaxial right circular cylinder; sphere outside end of cylinder, and sphere radius less than cylinder radius. Click to open calculator >>
132. Sphere to interior surface of coaxial right circular cylinder; sphere within ends of cylinder. Click to open calculator >>
133. Sphere to exterior of coaxial cylinder. Click to open calculator >>
134. Large sphere to small cylinder. r>> diameter or length of cylinder. Click to open calculator >>
135. Concentric spheres. Click to open calculator >>
136. Differential or finite areas on the inside of a spherical cavity. Click to open calculator >>
137. Two spheres of unequal radius. Click to open calculator >>
138. Sphere to spherical cap. Click to open calculator >>
139. Sphere to coaxial cone. Click to open calculator >>
140. Large sphere to small hemisphere (not including circular base). Click to open calculator >>
140a. Two directly opposed spherical caps on a common axis.
140b. Spherical cap on a sphere of radius r to itself and to its base
140c. Two complementary spherical caps on the same sphere of radius r.
140d. Two spherical caps of different size in the same sphere of radius r
140e. Euclidian spherical spiral with uniform spiral band.
140f. Logarithmic spherical spiral band.
141. Sphere to coaxial paraboloid. Click to open calculator >>
142. Sphere to coaxial ellipsoid. Click to open calculator >>
143. Large sphere to small ellipsoid. Click to open calculator >>
144. Ring area on inside of sphere to coaxial ring area on inside of attached frustum. Click to open calculator >>
145. Ring area on inside of sphere to ring on interior of cylinder attached to sphere by a conical frustum. Click to open calculator >>
146. Any finite area of any shape on interior of hemisphere to entire base. Click to open calculator >>
147. Spherical cap to disk in equatorial plane. Click to open calculator >>
148. Interior finite section of hemisphere to itself. Click to open calculator >>
149. Finite section on interior of hemisphere to parallel finite section. Click to open calculator >>
150. Section of interior of hemisphere to disk on base. Click to open calculator >>
151. Finite section of interior of hemisphere to disk on base. Click to open calculator >>
152. Section of hemisphere to annular ring in base. Click to open calculator >>
153. Ring on hemispherical surface to ring on the base. Click to open calculator >>
154. Two hemispheres in contact. Click to open calculator >>
155. Moebius strip of constant width to itself. Click to open calculator >>
155a. Spiral strip on inside of right circular cylinder to itself Click to open calculator >>
156. Seated standard person facing vertical panel. Click to open calculator >>
157. Seated standard person to side vertical rectangle. Click to open calculator >>
158. Seated standard person to rectangle on ceiling or floor. Click to open calculator >>
159. Standard standing person to rectangle on ceiling. Click to open calculator >>
160. Standing standard person to side vertical rectangle. Click to open calculator >>
161. Standing standard person to vertical facing rectangle. Click to open calculator >>
162. Pig to rectangle in various orientations. Click to open calculator >>
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