Question

If the height and the base area of a right circular cone are $5cm$ and $48c{m}^2$respectively, then the volume of the cone is equal to

Answer 1

Step $1$ : Compute the radius of the cone.

Given : height $\left(h\right)=5cm$ , Area $\left(A\right)=48c{m}^2$

We know that, area of the base of cone which is a circle is given by,

$$\begin{gathered} A={\mathrm{\pi r}}^2 \\ \Rightarrow r=\sqrt{\frac{48}{\mathrm{\pi }}} \end{gathered}$$

$\Rightarrow r=3.9cm$

Step $2$ : Compute the volume of the cone.

We know that, volume of the cone is given by,

$$\begin{gathered} v=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow \mathrm{v}=\frac{1}{3}\mathrm{\pi }{(3.9)}^2\left(5\right) \\ \Rightarrow \mathrm{v}=\frac{1}{3}\times \frac{22}{7}\times {(3.9)}^2\times 5 \\ \Rightarrow \mathrm{v}=79.89 \end{gathered}$$

$\Rightarrow v\approx 80c{m}^3$

Hence, the volume of the cone is equal to $80c{m}^3$.