Question

AB and CD are two perpendicular diameters of a circle with centre O,OD is the diameter of smaller circle.If OA =7 cm,then the area of the shaded region in figure,is

• A. $66.5{cm}^2$
• B. $66{cm}^2$
• C. $65{cm}^2$
• D. $67.5{cm}^2$

Answer 1

The correct option is A $66.5{cm}^2$

Radius of bigger circle $r_1=OA=7$
Radius of smaller circle $r_2=\frac{r_1}{2}$
$=\frac{7}{2}$
Area of the bigger circle $C_1=\pi {r_1}^2$
$=\frac{22}{7}\times 7\times 7$
$=154c{m}^2$
Area of the semicircle $=\frac{154}{2}c{m}^2$
$=77c{m}^2$
Area of the smaller circle $C_2=\pi {r_2}^2$
$=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$
$=\frac{77}{2}$
Area of the unshaded triangle $△ABC=\frac{1}{2}\times AB\times OC$
$=\frac{1}{2}\times 14\times 7$
$=49c{m}^2$
$\therefore$ Area of the shaded portion $=$Area of the smaller circle +(Area of semicircle -Area of the triangle $△ABC$)
$=\frac{77}{2}+(77-49)$
$=66.5c{m}^2$