Question

If the volume of a right circular cone of height $9\mathrm{cm}$ is $48{\mathrm{\pi cm}}^3$, find the diameter of its base.

Answer 1

Calculate the diameter of base of right circular cone.

The volume of a cone is one-third of the product of the area of the base and the height of the cone. The volume is measured in terms of cubic units.

Volume of a right circular cone can be calculated by the following formula,

$\mathit{V}\mathbf{=}\frac{\mathbf{\pi }{\mathbf{r}}^{\mathbf{2}}\mathbf{h}}{\mathbf{3}}$

Here, $V$ is volume of cone, $\mathrm{h}$ is height of cone, $\mathrm{r}$ is the radius of base.

To find the diameter of the cone, we will first find the radius of the cone.

From the given,

$V=48\mathrm{\pi }{\mathrm{cm}}^3$

$\mathrm{h}=9\mathrm{cm}$

So,

$\Rightarrow$ $48\mathrm{\pi }=\frac{1}{3}{\mathrm{\pi r}}^2\times 9$

$\Rightarrow$ $48\mathrm{\pi }=\frac{1}{3}{\mathrm{\pi r}}^2\times 9$

$\Rightarrow$ $48=\frac{1}{3}{r}^2\times 9$

$\Rightarrow$ $r^2=\frac{48\times 3}{9}$

$\Rightarrow$ $r^2=16$

$\Rightarrow$ $r=4$

We know that,

$\mathbf{Diameter}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{radius}$

$\Rightarrow$ $\mathrm{Diameter}=2\times 4$

$\Rightarrow$ $\mathrm{Diameter}=8$

Hence, the diameter of the base of right circular cone is $8\mathrm{cm}$.