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,

Substituting the value of radius,

Hence, the area of OACB is.

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

Let the area of quadrant of small circle be.

It is clear from the above figure that area of shaded region is the difference of larger quadrant and the smaller one. Hence,