Question

Find the area of the shaded sector of the circle having radius = 21 cm. (Use $=\pi \frac{22}{7}$)

• A. $192.5c{m}^2$
• B. $385c{m}^2$
• C. $462c{m}^2$
• D. $539c{m}^2$

Answer 1

The correct option is B $385c{m}^2$

Given:
r = 21 cm
In a circle, total angle around the centre $={360}^o$
$\Rightarrow 20+2m+2m+40={360}^o$

$\Rightarrow m=\frac{{200}^o}{4}$

$\Rightarrow m={50}^o$

$\therefore$ Angle of shaded sector $=2\times 50={100}^o$

Thus, area of shaded sector
$=\frac{\theta }{360}\times \pi r^2$
$=\frac{100}{360}\times \frac{22}{7}\times 21\times 21$
$=385c{m}^2$

Area of the shaded sector $=385c{m}^2$