In the following figure, the area of the shaded region is

Question:

In the following figure, the area of the shaded region is

(a) $3 \pi \mathrm{cm}^{2}$

(b) $6 \pi \mathrm{cm}^{2}$

(c) $9 \pi \mathrm{cm}^{2}$

(d) $7 \pi \mathrm{cm}^{2}$

Solution:

In the figure,

$\angle C=\angle B=90^{\circ}$ and $\angle D=60^{\circ}$,

$\therefore \angle A+\angle B+\angle C+\angle D=360^{\circ}$

$\angle A+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}$

$\therefore \angle A=120^{\circ}$

Area of shaded region $=\frac{\theta}{360} \times \pi r^{2}$

$\therefore$ Area of shaded region $=\frac{120}{360} \times \pi \times 3^{2}$

$\therefore$ Area of shaded region $=\frac{1}{3} \times \pi \times 9$

$\therefore$ Area of shaded region $=3 \pi$

Therefore, area of the shaded region is $3 \pi \mathrm{cm}^{2}$

Hence, the correct answer is option (a).

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