Example.—Required the content of a sphere, whose axis is 12.
12 × 12 × 12 × ·5236 = 904·7808. Content required.
To find the solidity of an hemisphere.
Find the solidity of the sphere, and half the content will be that of the hemisphere.
Note 1.—Any sphere, or globe twice the diameter of another contains four times the superficies, or area of the other, and eight times the solid content. Hence the superficies of spheres are as the squares, and the solidity as the cubes of their diameters.
Note 2.—The cube of the diameter of a sphere in inches, multiplied by ·00188, will give the number of imperial gallons it will contain.
To find the solid content of a spherical segment.
1. From three times the diameter of the sphere, take double the height of the segment; then multiply the remainder by the square of the height, and this product by ·5236.
2. Or, to three times the square of the radius of the segment’s base add the square of its height; then multiply the sum by the height, and the product by ·5236.