Question

In the following Figure, AB and CD are two diameters of a circle that are perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

• A. 162$c{m}^2$
• B. 125.3 $c{m}^2$
• C. 110 $c{m}^2$
• D. 115 .5 $c{m}^2$

Answer 1

The correct option is D

115 .5 $c{m}^2$

It is given that, OA = 7 cm

So, radius r of smaller circle will be

r = $\frac{7}{2}$

= 3.5 cm

Hence area of the smaller circle= = $\pi$ x $r^2$

= $\frac{22}{7}$ x r x r

= $\frac{22}{7}$ x 3.5 x 3.5

= 38.5 $c{m}^2$

Radius of the larger circle = 7 we have

Area of the larger circle = $\frac{22}{7}$ x 7 x 7

= 154 $c{m}^2$

Area of the shaded region = Area of the larger circle – Area of the smaller circle

= 154 - 38.5

= 115 .5 $c{m}^2$

Hence required area 115.5cm²