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If a cylinder has the same height as a square prism, and have equal lateral surface area, what would be the ratio of the cylinder to ratio of the square prism?

So from my understanding, a square prism must have at least two square sides. In this case, how would I know which sides would be square and which sides wouldn't? Would it just be the top and base of the prism that would be square? So for the lateral surface area of a prism, I need to add the area of the four sides, so would that just be $4\times h\times a$; where $h$ is height and $a$ is one of the sides of the square base?

Thanks for your help!

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1 Answer

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The lateral surface area of a cylinder or prism is the surface area that is not the ends. It is the product of the perimeter of the base and the height. Given that the heights are equal, the perimeters of the bases must be equal.

The volume of the cylinder or prism is the area of the base times the height. You are being asked for the ratio of areas of a square and circle that have equal perimeter.

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