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:
a. x^3 - x^2(h-2)
b. x^2-1/3x^2h
c. 1/3x2^h
d. 2/3x^2h
e. x^2(h+2) - 1/3x^2h

Answer 1

Volume of a pyramid is one-third the volume of the prism it fits in, so you have empty space equal to the prism the pyramid would fit in minus the volume of the pyramid, plus a rectangular prism of space which is x by x by 2in.

Answer 2

The prism that the pyramid would just fit in is x by x by h (=hx^2). The volume of the pyramid is one-third of that (=hx^2/3). The additional space above is x by x by 2 (=2x^2).
Can you get it from there?

Answer 3

so choice e.?

Answer 4

Yeah, that seems to work.

Answer 5

ok, thanks alot!