Question

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

Answer 1

It is given that, OA = 7 cm

So, radius r of small circle will be

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

= 3.5 cm

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

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

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

= 38.5 $c{m}^2$

Now, let the area of large circle be. A

Now we know that the area of a circle = $\pi$ $r^2$

Substututing the value of r= 7 we have

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

Hence Area of the large circle= 154 $c{m}^2$

,

Area of the shaded region = Area of the large circle – Area of the small circle

= 154- 38.5

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

​​​Hence required area 115.5cm²