Question

The equation above can be used to calculate the volume V, of a cone with a height h and radius r. If the volume of a cone is 243?ft3, and the height is equal to the radius of the base, what is the height of the cone in feet?

Answer 1

The height of the cone is
`h=9\ ft`

Explanation:

we know that

The volume of a cone is equal to

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

In this problem we have

`V=243\pi\ ft^(3)`

`r=h\ ft`

substitute

`243\pi=(1)/(3)\pi (h^(2))h`

simplify

`729=(h^(3))`

`h=\sqrt[3]{729}\ ft`

`h=9\ ft`