Question

From a circle of radius $15cm$., a sector with angle ${216}^o$ is cut out and its radii are bent so as to form a cone. Find its volume.

Answer 1

Solution:-

Let 'r' be the radius of the base, 'l' be the slant height, i.e., the radius $(R=15cm)$ of the sector with $216°$ angle

The sectoral arc becomes the perimeter of the base circle.

$\therefore 2\pi r=\left(\frac{216}{360}\right)2\pi R$

$\Rightarrow \frac{r}{R}=\frac{216}{360}$

$\Rightarrow \frac{r}{15}=\frac{216}{360}$

$\Rightarrow r=\frac{216}{360}\times 15=9$

From pythagoras theorem,

$h^2=l^2-r^2$

$h^2=225-81=144$

$h=\sqrt{144}=12$

$\therefore volume=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi \times 9^2\times 12=27\times \pi \times 12=1017.87{cm}^3$