Answer: The answers are equal and [tex]\pi r^2h.[/tex]
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 [tex]\pi r^2[/tex] .
The area of the base of the cylinder and every cross section parallel to its base is [tex]\pi r^2[/tex] .
By Cavalieri's principle, this rectangular prism and this cylinder have equal volumes.
The volume of the rectangular prism is [tex]\pi r^2h.[/tex]
Therefore, the volume of the cylinder is [tex]\pi r^2h.[/tex]
Thus, the steps are completed.
