In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
In Fig. 12.30, 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.

Solution:

Quadrants’ radius = 3.5 cm or 7/2 cm

(i) The area of the quadrant OACB = (πR2)/4 cm2

= (22/7)×(7/2)×(7/2)/4 cm2

= 77/8 cm2

(ii) The area of triangle BOD = (½)×(7/2)×2 cm2

= 7/2 cm2

Area of quadrant – Area of triangle BOD = Area of shaded region

= (77/8)-(7/2) cm= 49/8 cm2

= 6.125 cm2