Question

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

Answer 1

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.

Answer 2

all three have the same volume

Explanation:

Cavalieri's principle states that if the areas of the cross sections of two solids are equal, and the height of the two solids are equal, then the volumes of the two solids are equal.