Question

The radius of a sector is $12cm$ and angle is ${120}^o$. By coinciding its straight sides, a cone is formed. Find the volume of that cone.

Answer 1

Given radius of the sector $=12\text{cm}$

and $\theta$ $={120}^{\circ }$

If a cone is formed by joining its straight sides, then height of cone $=$ radius of sector $=12\text{cm}$

and Perimeter of circular part of the cone = length of arc

Let '$r$' be radius of cone, then

$2\pi r=2\pi \times 12\times \frac{120}{360}$

$r=4\text{cm}$

So, radius of the cone $=4\text{cm}$ and height of the cone $=12\text{cm}$

Then,

Volume of the cone $=\frac{1}{3}\pi r^{2}h$

Volume of the cone $=\frac{1}{3}\times 3.14\times 16\times 12$

Volume of the cone $=64\pi {\text{cm}}^3$