Question

A cone and a cylinder have the same radius and height. The volume of the cone is 100π (pi) cubic feet. What is the volume of the cylinder?

Answer 1

The volume of the cylinder is
`300\pi` cubic feet.

Explanation:

From Geometry we remember that volumes of a cone and a cylinder with the same radius (
`R`), measured in feet, and height (
`h`), measured in feet, are defined by the following equations:

Cone

`V_(co) = (1)/(3)\pi\cdot R^(2)\cdot h` (1)

Cylinder

`V_(cy) = \pi\cdot R^(2)\cdot h` (2)

The ratio of the volume of the cylinder to the volume of the cone is:

`(V_(cy))/(V_(co)) = 3` (3)

If we know that
`V_(co) = 100\pi\,ft^(3)`, then the volume of the cylinder is:

`V_(cy) = 3\cdot V_(co)`

`V_(cy) = 300\pi\,ft^(3)`

The volume of the cylinder is
`300\pi` cubic feet.