Question

A cone is placed inside a cylinder as shown. The radius of the cone is half the radius of the cylinder. The height of the cone is equal to the radius of the cylinder. What is the volume of the cone in terms of the radius, r?

Answer 1

The volume of a cone is 1/3 pi R^2 H where R = radius of the base of the cone and hH= height of the cone

her H = r and R = 0.5r so the volume of the cone is
1/3 * pi * (0.5r)^2 * r

= 1/3 * pi * 0.25 r^3

= (1/12) pi r^3 Answer

Answer 2

Volume of the cone is
`(1)/(12)\pi r^(3)`

Explanation:

Formula to find the volume of a cone is V =
`(1)/(3)\pi r^(2)h`

Here r is the radius of the cone and h is the height of the cone.

Since radius of cone =
`(1)/(2)(\text{Radius of cylinder})`

=
`(r)/(2)`

Height of the cone = radius of the cylinder = r

Now we put the values of radius and height of cone in the formula

Volume of cone =
`(1)/(3)\pi ((r)/(2))^(2)(r)`

=
`(1)/(3)\pi((r^(2))/(4))(r)`

=
`(1)/(12)\pi r^(3)`

Therefore, volume of the cone is
`(1)/(12)\pi r^(3)`