Question

In the given figure, OACB is a quadrant of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the

(i) Quadrant OACB

(ii) Shaded region

[Use Π = 22/7]

Answer 1

(i) Since OACB is a quadrant, it will subtend 90° angle at O.

Area of quadrant OACB = `90^@/360^@ xx pir^2`

`=1/4xx22/7xx(3.5)^2 = 1/4xx22/7xx(7/2)^2`

`= (11xx7xx7)/(2xx7xx2xx2) = 77/8 cm^2`

(ii) Area of ΔOBD = 1/2 x OB x OD

`= 1/2xx3.5xx2`

`= 1/2xx7/2xx2`

`= 7/2 cm^2`

Area of the shaded region = Area of quadrant OACB − Area of ΔOBD

`= 77/8-7/2`

`= (77-28)/8`

`= 49/8 cm^2`