Question

A rectangular display case houses a square pyramid. Both have the same square base measuring x inches on a side. The top of the case is 2 inches above the tip of the pyramid which has a height of h inches. Which expression represents the volume of the empty space inside the case?

Answer 1

The rectangular display case has volume (x)(x)(h+2) = x^2h + 2 x^2.

The housed pyramid has volume 1/3 B h = 1/3 (x*x) h= 1/3x^2h.

Empy Space = Case volume - pyramid volume =

x^2 h + 2 x^2 - 1/3 x^2 h = x^2 h - 1/3 x^2 h + 2 x ^2 =

[ (2/3) x^2 h + 2 x ^ 2] cubic inches --> Please check my work.