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

directrix · Answer

The display case has volume Bh where B is the area of the base and h is the height of the rectangular case. 

The pyramid has base area the same as that of the case. Its volume = (1/3) B ( h -2) given that the pyramid's height is two shorter than that of the case.

The volume of the empty space is Bh - (1/3)* B* (h - 2)=  (2/3) Bh + (2/3)B