Question

OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.

Answer 1

Given,

Radius of small quadrant, r = 2 cm

Radius of big quadrant, R = 3.5 cm

(i) Area of quadrant OACB = 1/4 πR2

= 1/4 (22/7)(3.5)2

= 269.5/28 = 9.625 cm2

(ii) Area of shaded region = Area of big quadrant – Area of small quadrant

= 1/4 π(R2 – r2)

= 1/4 (22/7)(3.52 – 22)

= 1/4 (22/7)(12.25 – 4)

= 1/4(22/7)(8.25)

= 6.482 cm2