Question

A semicircle is drawn with $AB$ as its diameter. From $C$, a point on $AB$, a line perpendicular to $AB$ is drawn melting the circumference of the semicircle at $D$. Given that $AC$ $=$ $2$ cm. and $CD$ $=$ $6$ cm, the area of the semicircle is -

• A. $60$ $\pi$
• B. $50$ $\pi$
• C. $40$ $\pi$
• D. $32$ $\pi$

Answer 1

The correct option is B $50$ $\pi$

$OC=r-2$
$(r-2{)}^2+6^2=r^2\Rightarrow r=10$
Semicircle area $=\frac{\pi r^2}{2}=50\pi c{m}^2$