A square prism and a cylinder have the same height. The area of the cross-section of the square prism is 157 square units, and the area of the cross-section of the cylinder is 50π square units. Based on this information, which argument can be made?

Question

Vocaloid · Answer

choices

-The volume of the square prism is one third the volume of the cylinder.
-The volume of the square prism is half the volume of the cylinder.
-The volume of the square prism is equal to the volume of the cylinder.
-The volume of the square prism is twice the volume of the cylinder.

Vocaloid · Answer

This isn't really the best-worded question, but let's make some simplifying assumptions

- let's assume they are talking about cross-sections parallel to the base in both cases. that way, we can use volume = bh to compare
- let's use pi = 3.14

that way, 50pi = 157 and thus both cross-sections are equal

both of these shapes have volume = base*height. since the bases are equal (equal cross-sections) and the heights are also equal, what does that tell you about their volumes?