Question:
In the following figure, the shaded area is
(a) $50(\pi-2) \mathrm{cm}^{2}$
(b) $25(\pi-2) \mathrm{cm}^{2}$
(c) $25(\pi+2) \mathrm{cm}^{2}$
(d) $5(\pi-2) \mathrm{cm}^{2}$
Solution:
Area of the shaded region is-
$=\left[\frac{\pi \theta}{360}-\sin \frac{\theta}{2} \cos \frac{\theta}{2}\right](r)^{2}$
$=\left(\frac{\pi}{4}-\frac{1}{2}\right)(10)^{2}$
$=25(\pi-2) \mathrm{cm}^{2}$
So the answer is (b).