Question

A sector containing an angle of ${120}^{\circ }$ is cut off from a circle of radius $21$ cm and folded into a cone by joining the radii. Find the curved surface area of the cone. $(\pi =\frac{22}{7})$

Answer 1

Given, radius of the circle $r=21$ cm

Since the cone is formed by folding a sector it's curved surface area is equal to the area of the sector.

Area of sector subtending angle $\theta$ $=$ $\frac{\theta }{360}\times \pi r^2$

Area of sector $=$ $\frac{120}{360}\times \pi r^2$ .....($\because$ angle subtended by sector is ${120}^o$)

$=$ $\frac{1}{3}\times \frac{22}{7}\times 21\times 21c{m}^2$

$=$ $462{\text{cm}}^2$

Hence, curved surface area of the cone is $462{\text{cm}}^2$