The equation above can be used to calculate the volume V, of a pyramid with a height h and base with length l and width w. If the volume of a pyramid is 81inches^3, and l=w=3h, what is the length of the base of the pyramid in inches?

Comment

The formula for a pyramid = (1/3) L * W * h The base in this case is square.

Givens

L = W

W = W

L = 3H

H = L/3 = (1/3L)

V = 81 in^3

Solve

V = 1/3 L * W * H

V = 1/3 L * L * 1/3 L

81 = 1/9 L^3 Multiply through by 9

81 * 9 = L^3

729 = L^3 Take the cube root of both sides.

cube root (L^3) = cube root (729)

L = 9 in

Volume of a pyramid is V = lwh/3

You know

V=81

l=3h

w=3h

h=3

l=9

w=9

So length is 9 inches