Question

in the figure OACD is a quadrant of a circle with centre O and radius 3.5cm if OD=2cm find the area of the shaded region​

Answer 1

SOLUTION:-

Given,

Radius= 3.5cm

Since OACB is a quadrant, it will subtend 90° angles at O.

Area of quadrant OACB

$= > \pi {r}^{2} \times \frac{90 \degree}{360 \degree} \\ \\ = > \frac{22}{7} \times ( \frac{7}{2} ) {}^{2} \times \frac{1}{4 } \\ \\ = > \frac{11 \times 7 \times 7}{2 \times 7 \times 2 \times 2} = > \frac{77}{8} {cm}^{2}$

Area of ∆OBD,

$= > \frac{1}{2} \times OB\times OD\\ \\ = > \frac{1}{2} \times 3.5 \times 2 \\ \\ = > \frac{1}{2} \times \frac{7}{2} \times 2 \\ \\ = > \frac{7}{2} {cm}^{2}$

Area of the shaded region;

Ar. of quadrant OACB - Ar. of ∆OBD

$= > \frac{77}{8} - \frac{7}{2} \\ \\ = > \frac{77 - 28}{8} \\ \\ = > \frac{49}{8} {cm}^{2}$

Hope it helps ☺️