Question

Two square pyramids have the same volume. For the first pyramid, the side length of the base is 15 in., and the height is 18 in. The second pyramid has a height of 54 in. What is the side length of the base of the second pyramid?

Answer 1

Volume for a square pyramid uses the formula V = a^2 x h/3

Volume for the first pyramid = 15^2 x 18/3 = 225 x 6 = 1350 cubic inches.

The second pyramid has the same volume, so we can use the volume from the first one to solve for the side length:

Second pyramid: 1350 = a^2 x 54/3

1350 = a^2 x 18

a^2 = 1350 / 18

a^2 = 75

a = √75 = 8.66 inches