Question

The central angle and radius of a sector of a circular disc are ${180}^o$ and $21$ cm respectively. If the edges of the sector are joined together to make a hollow cone, then find the radius of the cone.

Answer 1

Area of the sector $=\frac{\theta }{{360}^o}\times \pi r^2$ square
$=\frac{{180}^o}{{360}^o}\times \frac{22}{7}\times 21\times 21$ ....$(R=2$ cm $)$
$=693c{m}^2$
C.S.A. of cone $=$ Area of the sector
$\Rightarrow \pi rl=693$ ....$(r:l=R)$
$\Rightarrow \frac{22}{7}\times r\times 21=693$
$\Rightarrow r=693\times \frac{1}{3}\times \frac{1}{22}=\frac{21}{2}=10.5$ cm