In the following figure, 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.
It is given that AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of small circle.
It is given that, $\mathrm{OA}=7 \mathrm{~cm}$'
So, radius r of small circle is
$r=\frac{7}{2} \mathrm{~cm}$
$=3.5 \mathrm{~cm}$
We know that the area $A$ of circle of radius $r$ is $A=\pi r^{2}$.
Substituting the value of $r$ in above formula,
$A=\frac{22}{7} \times 3.5 \times 3.5$
$=38.5 \mathrm{~cm}^{2}$
Now, let the area of large circle be $A^{\prime}$.
Using the value radius $\mathrm{OA}$,
$A^{\prime}=\frac{22}{7} \times 7 \times 7$
$=154 \mathrm{~cm}^{2}$
Hence,
Area of shaded region =Area of large circle - Area of small circle
$=154-38.5$
$=115.5 \mathrm{~cm}^{2}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.