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?

Question

anonymous · Answer

Hi! :) The volume of the rectangular display case is actually (area of base * height) = (x^2)(h+2). The volume of the square pyramid is (1/3)(area of base * height) = (1/3)(x^2)(h). Since the rectangular prism houses the pyramid, we can just subtract the volume of the thing inside from the volume of the casing to get the space in between.

Can you do it now?