Question

A square pyramid has a height h and a base with side length b. The side lengths of the base increase by 50%. Write a simplified expression that represents the volume of the new pyramid in terms of b and h.

Answer 1

The general formula for the volume of a square pyramid is

V = (1/3)b^2 h

If b increase by 50% their new length = 3b/2

Therefore the volume of the new pyramid is

V = (1/3) (3b/2)^2 h

= (1/3) 9b^2 / 4 h

= 3/4b^2 h Answer