Q:

Based on the graphic, which three-dimensional figure has the greatest volume?

Accepted Solution

A:
Using the assumptions that the prisms have a square base and that the side of the square is the same length as the diameter:
The first prism would have a volume of s²h.  
The second prism, under Cavalieri's principle, would have the same area as the first (if they have the same cross-sectional area and same height, they have the same volume).
The cylinder at the end would have a volume of π(r²)h = π(1/2s)²h = π(1/4s²)h = 1/4πs²h.  1/4 of π is less than 1, so that means the cylinder would have the smallest volume.