Question

A sector containing an angle of 120 degree is cut off from a circle of radius 21 cm and folded into a cone. Find the curved surface area of a cone.

• A. $442c{m}^2$
• B. $462c{m}^2$
• C. $362c{m}^2$
• D. $262c{m}^2$

Answer 1

The correct option is B $462c{m}^2$

The cone is being created by joining the radius. So the radius of the sector is going to be the slant height of the cone.

Slant height (L) = 21 cm

Arc length of the sector = Circumference of the base of the cone

Length of arc = $\frac{\theta }{360}\times 2\pi R$
Here R represents radius of the sector.

So, length of arc = $\frac{120}{360}\times 2\times \frac{22}{7}\times 21$
= $\frac{1}{3}$ x 2 x 22 x 3
= 44 cm

So, circumference of the base of the cone = 44 cm
Let radius of the base of cone be r.
Then, $2\pi r$ = 44
$\Rightarrow 2\times \frac{22}{7}\times r$ = 44
$\Rightarrow r$ = $44\times \frac{1}{2}\times \frac{7}{22}$
$\Rightarrow r$ = 7 cm

Now, we need to find the curved surface area of cone

CSA of cone = $\pi rl$
$\Rightarrow \frac{22}{7}\times 7\times 21$
$\Rightarrow 462c{m}^2$

Hence, curved surface area of the cone is 462 cm².