Question

the volume of a right cone is 27 π units^3. if its height is 9 units find its circumference in terms of π.

Answer 1

Given:

the volume of a right cone is 27 π units³

And the height of the cone = h = 9 units

First, we will find the radius of the base (r) using the formula of the volume.

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

Substitute V = 27π and h = 9

`27π=(1)/(3)πr^2(9)`

Solve the equation to find (r)

`\begin{gathered} r^2=(3*27)/(9)=9 \\ r=√(9)=3 \end{gathered}`

Now, we will find the circumference using the following formula:

`circumference=2πr`

substitute r = 3

`circumference=2π(3)=6π`

So, the answer will be: Circumference = 6π units