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

Question

In Fig., 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

Given, 

Area of quadrant OACB = \(\frac{θ}{360}πr^2\)

= \(\frac{90}{360}\times\frac{22}7\times3.5\times3.5\)

= \(\frac{1}{4}\times11\times3.5\) = 9.635 cm²

Area of shaded region = area of quadrant OACB – area of quadrant ODEF

= 9.625 - \(\frac{90}{360}\times\frac{22}{360}\times2\times2\)

= 9.625 - \(\frac{1}{4}\times3.14\times4\)

= 6.485 cm²