the base by the perpendicular let fall from the vertex upon the base, and divide by 3.
To find the solid content of a prism. Multiply the area of the base by the perpendicular distance between the opposite bases.
To find the surface of a sphere. Multiply 4 times the square of the radius by 3·1415927.
To find the solid content of a sphere. Multiply the cube of the radius by 3·1415927 × ⁴/₃, or 4·18879.
To find the surface of a right cone. Take half the product of the circumference of the base and slanting side. To find the solid content, take one-third of the product of the base and the altitude.
To find the surface of a right cylinder. Multiply the circumference of the base by the altitude. To find the solid content, multiply the area of the base by the altitude.
The weight of a body may be found, when its solid content is known, if the weight of one cubic inch or foot of the body be known. But it is
usual to form tables, not of the weights of a cubic unit of different bodies, but of the proportion which these weights bear to some one amongst them. The one chosen is usually distilled water, and the proportion just mentioned is called the specific gravity. Thus, the specific gravity of gold is 19·362, or a cubic foot of gold is 19·362 times as heavy as a cubic foot of distilled water. Suppose now the weight of a sphere of gold is required, whose radius is 4 inches. The content of this sphere is 4 × 4 × 4 × 4·1888, or 268·0832 cubic inches; and since, by (217), each cubic inch of water weighs 252·458 grains, each cubic inch of gold weighs 252·458 × 19·362, or 4888·091 grains; so that 268·0832 cubic inches of gold weigh 268·0832 × 4888·091 grains, or 227½ pounds troy nearly. Tables of specific gravities may be found in most works of chemistry and practical mechanics.
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