Question

consider a right rectangular prism and a right cylinder with the same height and base area. according to cavalieris principle, what must be true about the cross - sectional areas at any level?
the cross - sectional areas of the prism and cylinder will be equal at every level.
the cross - sectional areas of both solids will vary depending on their height.
the cross - sectional areas of the prism will be larger than those of the cylinder.
the cross - sectional areas of the cylinder will be larger than those of the prism

Explanation:

Cavalieri's principle states that if two solids have the same height and the same cross - sectional area at every level, then they have the same volume. Here, the right rectangular prism and the right cylinder have the same height and base area. Since the cross - sectional area of a right rectangular prism at any level (parallel to the base) is equal to its base area (because it's a prism with uniform cross - section), and the cross - sectional area of a right cylinder at any level (parallel to the base) is equal to its base area (because it's a cylinder with uniform cross - section).

Answer:

The cross - sectional areas of the prism and cylinder will be equal at every level.