To find the diameter of a leaden ball, its weight being given.
To 4 times the weight add half the weight, and 3/100 of half the weight; and the cube root of this sum will be the diameter in inches, nearly.
Example.—What is the diameter of a leaden ball, whose weight is 8 pounds?
8 x 4 = 32 8 2 = 4 3 100 of 4 = ·12.
32 + 4 + ·12 = 36·12, of which the cube root is 3·3 inches, nearly.
Diameter required.
To find the weight of an iron shell, its interior and exterior diameter being given.
Take 9 64 of the difference of the cubes of the external and internal diameters, for the weight of the shell in pounds.
Example.—What is the weight of a shell whose exterior diameter is 12·85 inches, and interior diameter 8·75 inches?
12·85 cubed = 2121·8241, 8·75 cubed = 669·9218.
2121·8241 - 669·9218 = 1451·9022.
9 64 of 1451·9022 = 204·1737 pounds. Weight required.
To find the quantity of powder a shell will contain.
Divide the cube of the interior diameter in inches by 57·3, and the quotient will be the weight in pounds.