Question

In Fig., $AB$ and $CD$ are two diameters of a circle with centre $O$, which are perpendicular to each other. $OB$ is the diameter of the smaller circle. If $OA=7cm$, find the area of the shaded region. $[Use\pi =\frac{22}{7}]$

• A. $60.5c{m}^2$
• B. $63.5c{m}^2$
• C. $66.5c{m}^2$
• D. $56.5c{m}^2$

Answer 1

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

Radius of larger circle, $R=7$ cm

Radius of smaller circle, $r=\frac{7}{2}$ cm

Height of $\Delta BCA=OC=7$ cm

Base of $\Delta BCA=AB=14$ cm

Area of $\Delta BCA=\frac{1}{2}\times 7\times 14=49c{m}^2$

Area of larger circle $=\pi r^2=\frac{22}{7}\times (7{)}^2=154c{m}^2$

Area of larger semicircle $=\frac{154}{2}=77c{m}^2$

Area of smaller circle $=\pi r^2=\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2=\frac{77}{2}c{m}^2$

Area of the shaded region $=$ Area of larger circle $-$ Area of triangle $-$ Area of larger semicircle $+$ Areaof smaller circle

Area of the shaded region $=154-49-77+\frac{77}{2}=\frac{133}{2}=66.5c{m}^2$