Question

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

Answer 1

In circular cone,

Height of the cone $\left(h\right)=9cm$
Let the radius of the cone be $r$.
Volume of the cone $=48\pi c{m}^3$
$\Rightarrow \frac{1}{3}\pi r^{2}h=48\pi c{m}^3$

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

$\Rightarrow r^2\times 3cm=48c{m}^3$

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

$\Rightarrow r^2=16c{m}^2$

$\Rightarrow r=4cm$
Diameter of the base $=2\times 4cm=8cm$