Question

Calculate the area of the shaded region in the figure given (in sq units). [Approximate to the nearest whole number and use $\pi =\frac{22}{7}$.]

• A. 469

Answer 1

The correct option is A 469

The figure comprises two sectors: One inner sector, OAB, and one outer sector, OCD.

$\text{Area of a sector of a circle}=\frac{{\theta }^{\circ }}{{360}^{\circ }}\times \pi \times r^2$

Area of outer sector, OCD
$=\frac{140°}{360°}\times \pi \times 20\times 20$

$=\frac{140°}{360°}\times \pi \times 400\text{sq. units}$

Area of inner sector, OAB
$=\frac{140°}{360°}\times \pi \times 4\times 4$

$=\frac{140°}{360°}\times \pi \times 16\text{sq. units}$


So,
Area of shaded region = Area of OCD – Area of OAB

$=\frac{140°}{360°}\times \pi \times (400-16)$

$=\frac{7}{18}\times \frac{22}{7}\times 384=469.3\text{sq units}$

$\approx 469\text{sq units}$