Question

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

• A. $10.5cm$
• B. $10cm$
• C. $12.5cm$
• D. None of these

Answer 1

The correct option is A $10.5cm$

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 $\left(L\right)=21cm$

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

$=\frac{180}{360}\times 2\times \frac{22}{7}\times 21$

$=\frac{1}{2}\times 2\times 22\times 3$

$=66cm$

So, circumference of the base of the cone $=66$

$2\pi r=66$

$2\times \frac{22}{7}\times r=66$

$r=66\times \frac{1}{2}\times \frac{7}{22}$

$r=10.5cm$

Radius of the cone $=10.5cm$

Hence, this is the answer.