Question

In a circle of radius $10.5cm$, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

Answer 1

Radius of circle =$10.5cm$

Let $xcm$ be the major arc, then $\frac{x}{5}cm$ be the length of minor arc.

Circumference of circle = $x+\frac{x}{5}=\frac{6x}{5}$

We know, Circumference of circle = $2\pi r=2\times \frac{22}{7}\times 10.5$

This implies,

$\frac{6x}{5}=2\times \frac{22}{7}\times 10.5$

$x=55cm$

Area of major sector $=\frac{\text{length of arc}}{2\pi r}\times \pi r^2=\frac{1}{2}\times 55\times 10.5=288.75$

The area of major sector is $288.75c{m}^2$.