Question

Semicircular arcs $AO$ and $OB$ divide the circle above with centre $O$ into two regions. If the length of diameter $AB$ is $12$, calculate the area of the shaded region.

• A. $6\pi$
• B. $9\pi$
• C. $18\pi$
• D. $36\pi$

Answer 1

Answer: (C)

$18\pi$

Given, length of diameter $=12$
$\therefore AO=OB=6$
Area of Semi circle with diameter $AO$ is same as area of semi circle with diameter $OB$.
So, area of shaded region will be half the area of full circle.
As the area of circle is $=$ $\pi r^2$
$\pi {\left(\frac{12}{6}\right)}^2=\pi (6{)}^2=\pi \times 36$
Area of shaded region is $\frac{36\pi }{2}=18\pi$.