Question

How is the formula for the volume of a cylinder derived? Drag and drop the correct word into each box to complete the explanation.

The rectangular prism and the cylinder have .... heights.


The area of the base of the rectangular prism and every cross section parallel to its base is πr2 .


The area of the base of the cylinder and every cross section parallel to its base is πr2 .


By Cavalieri's principle, this rectangular prism and this cylinder have equal volumes.


The volume of the rectangular prism is πr2h .


Therefore, the volume of the cylinder is ....

Answer 1

Answer: The answers are equal and
`\pi r^2h.`

Step-by-step explanation: We are given the steps with some missing words for the derivation of the volume of a cylinder. The figure shows a rectangular prism and a cylinder.

The complete steps are as follows:

The rectangular prism and the cylinder have equal heights.

The area of the base of the rectangular prism and every cross section parallel to its base is
`\pi r^2` .

The area of the base of the cylinder and every cross section parallel to its base is
`\pi r^2` .

By Cavalieri's principle, this rectangular prism and this cylinder have equal volumes.

The volume of the rectangular prism is
`\pi r^2h.`

Therefore, the volume of the cylinder is
`\pi r^2h.`

Thus, the steps are completed.