To find the content of the solid part of a hollow cylinder.
From the content of the whole cylinder considered as a solid, subtract the content of the hollow part, also considered as a solid, and the difference will be the solidity required.
Example.—Required the content of the solid part of the hollow cylinder whose exterior diameter is 12 inches, the interior diameter 8 inches, and height 20 inches.
12 × 12 × ·7854 = 113·0976, area of base of cylinder.
113·0976 × 20 = 2261·952, solidity of whole cylinder.
8 × 8 × ·7854 = 50·2656, area of base of hollow cylinder.
50·2656 × 20 = 1005·312, content of hollow part.
2261·952 - 1005·312 = 1256·64 cubic inches. Solidity required.
To find the solidity of the frustrum of a cylinder.
Multiply the area of the base by half the greatest, and the least lengths, and the product will be the solidity.
Example.—Required the solidity of a frustrum, whose diameter is 24 inches, the greatest length 36 inches, and the least length 20 inches.
24 × 24 = 576. Square of the diameter.
576 × ·7854 = 452·3904. Area of the base.
452·3904 × (36 + 20) 2 = 12666·9312 Cubic inches. Solidity required.
To find the content of a pyramid, or cone.