Question

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.

 

Answer 1

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,

 ${\displaystyle A=\frac{1}{4}\pi r^2}$

Substituting the value of radius,${\displaystyle r=3.5c{m}^2}$

 ${\displaystyle A=\frac{1}{4}\times \frac{22}{7}\times 3.5\times 3.5}$

${\displaystyle =9.625c{m}^2}$

 

Hence, the area of OACB is${\displaystyle .9.625c{m}^2}$

(ii) It is given that radius of quadrant of small circle is 2 cm.

Let the area of quadrant of small circle be .A'

     ${\displaystyle A\prime \frac{1}{4}\pi r^2}$

${\displaystyle =\frac{1}{4}\times \frac{22}{7}\times 2\times 2}$

${\displaystyle =3.14c{m}^2}$

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'

${\displaystyle =9.625-3.14}$

${\displaystyle =6.485c{m}^2}$