In the following figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) quadrant OACB
(ii) shaded region.
It is given that OACB is a quadrant of circle with centre at O and radius 3.5 cm.
(i) We know that the area of quadrant of circle of radius r is,
$A=\frac{1}{4} \pi r^{2}$
Substituting the value of radius,
$A=\frac{1}{4} \times \frac{22}{7} \times 3.5 \times 3.5$
$=9.625 \mathrm{~cm}^{2}$
Hence, the area of $\mathrm{OACB}$ is $9.625 \mathrm{~cm}^{2}$.
(ii) It is given that radius of quadrant of small circle is 2 cm.
Let the area of quadrant of small circle be $A^{\prime}$.
$A^{\prime}=\frac{1}{4} \pi r^{2}$
$=\frac{1}{4} \times \frac{22}{7} \times 2 \times 2$
$=3.14 \mathrm{~cm}^{2}$
It is clear from the above figure that area of shaded region is the difference of larger quadrant and the smaller one. Hence,
Area of shaded region $=A-A^{\prime}$
$=9.625-3.14$
$=6.485 \mathrm{~cm}^{2}$