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,

 `A=1/4pir^2`

Substituting the value of radius,`r=3.5 cm^2`

 `A=1/4xx22/7xx3.5xx3.5`

`=9.625 cm^2`

 

Hence, the area of OACB is`.9.625cm^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'

     `A'1/4 pir^2`

`=1/4xx22/7xx2xx2`

`=3.14 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'

`=9.625-3.14`

`= 6.485 cm^2`