Question

In fig., $AB$ and $CD$ are two diameters of a circle (with centre $O$) perpendicular to each other and $OD$ is the diameter of the smaller circle. If $OA=14cm$, find the area of the shaded region

Answer 1

Area of Shaded region $=2\times$ Area of segment $BC$ (or Segment $AC$) $+$ Area of circle with diameter $DO$
Since, $DO=OC=BO=AO=7cm$
$\therefore$ Area of segment $BC$ $=$ Area of quadrant $BOC$ $-$ Area of $△$ $BOC$

$=\left(\frac{\pi \times 7\times 7}{4}\right)-(\frac{1}{2}\times 7\times 7)$

$=14c{m}^2$
Area of circle with diameter $OD$ $=\pi \times 3.5\times 3.5$

$=38.5c{m}^2$
$\therefore$ Area of Shaded region $=(2\times 14)+38.5$

$=66.5c{m}^2$