Question

In fig. seg $AB$ and seg $CD$ are perpendicular diameter of a circle with radius $7$ cm. Seg $AO$ is the diameter of smaller circle. Find the area of shaded region.

• A. $266$ $c{m}^2$
• B. $33.25$ $c{m}^2$
• C. $133$ $c{m}^2$
• D. $66.5$ $c{m}^2$

Answer 1

The correct option is D $66.5$ $c{m}^2$

Radius of small circle

$r_1$ $=\frac{d}{2}$$=\frac{OA}{2}$$=\frac{7}{2}cm$

Area of small circle

$\pi r_1^2$$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$$=\frac{77}{2}$$=38.5sqcm$

Radius of semicircle

$CO=7cm$

Area of semicircle

$\frac{1}{2}\pi r^2$$=\frac{1}{2}\times \frac{22}{7}\times 7\times 7$$=77sqcm$

In $△CBD$,

Base $=CD$$=2r$$=2\times 7$$=14cm$
Height $=OB=$ Radius $=7cm$

Area of $△CBD$

$\frac{1}{2}\times base\times height$$=\frac{1}{2}\times CD\times OB$
$=\frac{1}{2}\times 14\times 7$$=49sq.cm$

Area of shaded region $=$ Area of small circle $+$ Area of semicircle $-$ Area of $△CBD$
$=38.5+77-49$$=66.5sq.cm$