Question

In figure, $AB$ and $CD$ are two perpendicular diameters of a circle with centre $O$. If $OA$$=$$7cm$, find the area of the shaded region. [Use $\pi =\frac{22}{7}$]

• A. $31.4c{m}^2$
• B. $42.5c{m}^2$
• C. $54.2c{m}^2$
• D. $66.5c{m}^2$

Answer 1

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

Area of shaded region $=$ area of larger circle $-$ area of smaller circle $-$ area of the triangle

$=\pi R^2-\pi r^2-\frac{1}{2}\times DC\times BO$

$=\pi R^2-\pi r^2-\frac{1}{2}\times DC\times BO$

$=\frac{22}{7}(7^2-{\left(3.5\right)}^2)-\frac{1}{2}\times 14\times 7$

$=\frac{22}{7}(49-12.25)-49$

$=(\frac{22}{7}\times 36.75)-49$

$=115.5-49$

$=66.5$ ${cm}^2$