Question

A sector is cut from a circle of radius $21$ cm. The angle of the sector is ${150}^o$. Find the length of its arc and area.

• A. $27$ cm and $412.7c{m}^2$
• B. $36$ cm and $436.9c{m}^2$
  
• C. $45$ cm and $517.5c{m}^2$
  
• D. $55$ cm and $577.5c{m}^2$
  

Answer 1

The correct option is D $55$ cm and $577.5c{m}^2$

The length of arc $l$ and area $A$ of a sector of angle $\theta$ in a circle of radius $r$ are given by,

$l=\frac{\theta }{{360}^o}\times 2\pi r$

and $A=\frac{\theta }{{360}^o}\times \pi r^2$ respectively.

Here, $r=21$ cm and $\theta ={150}^0$

$\therefore l=\frac{150}{360}\times 2\times \frac{22}{7}\times 21=55$ cm

and

$A=\frac{150}{36}\times \frac{22}{7}\times {21}^2=\frac{1155}{2}=577.5{cm}^2$