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# In 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,

(i) Area of quadrant $$= \ \frac{1}{4} \ \pi r^2$$

$$= \ \frac{1}{4} \ × \ \frac{22}{7} \ × \ (3.5)^2$$

$$= \ \frac{1}{4} \ × \ \frac{22}{7} \ × \ ( \frac{7}{2} )^2 \ = \ \frac{77}{8}$$ cm2

(ii) Area of ∆ BOD = $$\frac{1}{2}$$ Base × Height

$$= \ \frac{1}{2} \ (OB \ × \ OD)$$

$$= \ \frac{1}{2} (3.5 \ × \ 2) \ = \ \frac{7}{2}$$ cm2

So, area of the shaded region

= Area of quadrant - Area of ∆ BOD

$$= \ \frac{77}{8} \ - \ \frac{7}{2} \ = \ \frac{49}{8}$$ cm2