Question

The volume of a right circular cone is 36 pi units^3 If the height of the cone is 12 units,what is the radius of the cone?

Answer 1

The radius of the cone is 3 units

Here, given the volume of a right circular cone and the height of the cone, we want to get the radius of the cone

Mathematically, we need the formula for the volume of a right circular cone

We have this formula as;

$V\text{ = }\frac{1}{3}\times\pi\times r^2\times h$

We substitute the value of the volume and the height as follows;

$\begin{gathered} 36\pi\text{ = }\frac{1}{3}\times\pi\times r^2\times12 \\ \frac{108\pi}{12\pi}=r^2 \\ \\ r^2\text{ = 9} \\ r\text{ = }\sqrt[]{9} \\ r\text{ = }\pm3\text{ units} \\ \text{radius cannot be negative so r = 3 units} \end{gathered}$