Example.—Required the upright surface of a triangular pyramid, the slant height being 20 feet, and each side of the base 3 feet.
3 + 3 + 3 = 9, perimeter of base.
9 × 20 2 = 90 feet. Surface required.
To find the surface of the frustrum of a pyramid, or cone.
Add together the perimeters of the two ends, multiply their sum by the slant height, and take half the product.
Example.—How many square feet are in the surface of the frustrum of a square pyramid, whose slant height is 10 feet, each side of the base 3 feet, and each side of the less end 2 feet.
3 + 3 + 3 + 3 = 12, perimeter of base.
2 + 2 + 2 + 2 = 8, perimeter of less end.
(12 + 8) × 10 2 = 100 feet. Surface required.
To find the solid content of a prism or cylinder.
Find the area of the base, or end, and multiply it by the length of the prism, or cylinder. Fora cube, multiply its side twice by itself; and for a parallelopipedon, multiply the length, breadth, and depth together for the content.
Example.—Required the solid content of a cube, whose side is 24 inches.
24 × 24 × 24 = 13824 square inches. Content required.