Question

The area of a sector of a circle of angle ${60}^{\circ }$ is $\frac{66}{7}c{m}^2$ then the area of the corresponding major sector is

• A. $14c{m}^2$
• B. $\frac{55}{7}c{m}^2$
• C. $\frac{110}{7}c{m}^2$
• D. $\frac{330}{7}c{m}^2$

Answer 1

Answer: (D)

$\frac{330}{7}c{m}^2$

Area of a sector of a circle of radius 'r' and angle $\theta =\frac{\theta }{360}\pi r^2$
Given, $\frac{60}{360}\times \frac{22}{7}\times r^2=\frac{66}{7}{cm}^2$
$r^2=18$
Now, area of sector with angle {300}^{o} $=\frac{300}{360}\times \frac{22}{7}\times r^2=\frac{300}{360}\times \frac{22}{7}\times 18=\frac{330}{7}{cm}^2$