Question

Fifteen cylinders and 15 rectangular prisms are stacked. Each cylinder has the same top surface area and height as each rectangular prism. What can you determine about the volumes of the two stacks of 15​ solids? Explain.

Choose the correct answer below.
A.
The two stacks have the same volume because they have the same height and width.
B.
The stack of prisms has a larger volume because the heights are the same and the circle can fit inside the​ rectangle, so it is smaller.
C.
The two stacks have the same volume because they have the same height and the same​ cross-sectional area at every level.
D.
The stack of cylinders has a larger volume because the heights are the same and a circle has a larger area than a rectangle with the same perimeter.

Answer 1

C. The two stacks have the same volume because they have the same height and the same cross-sectional area at every level

Explanation:

The volume of a cylinder can be found by multiplying the area of its base by its height.

Similarly, the volume of a rectangular prism can be found by multiplying the area of its base by its height.

Because they have the same base areas and the same heights, the same amount of each figure will result in the same volume from each stack.