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