Question

The following prism has a base area of 20\pi20π20, pi square units and a volume of 120\pi120π120, pi cubic units. The cylinder has the same base area and height. What is the volume of the cylinder?

Answer 1

Given:

A prism has a base area of $20\pi$ square units and a volume of $120\pi$ cubic units.

To find:

The volume of the cylinder if the cylinder has the same base area and height.

Solution:

Volume of a prism is:

$V=Bh$

Where, B is the base area and h is the height of the prism.

The volume of cylinder is:

$V=\pi r^2h$

$V=Bh$

Where, r is the radius, h is the height of the cylinder and $B=\pi r^2$ is the base area.

Since base area and height of the cylinder are same as the prism, therefore, there volumes are equal.

Hence the volume of the cylinder is $120\pi$ cubic units.