Question

The area of a semicircle of radius $4r$ is

• A. $8{\mathrm{\pi r}}^2$
• B. $4{\mathrm{\pi r}}^2$
• C. $12{\mathrm{\pi r}}^2$
• D. $2{\mathrm{\pi r}}^2$

Answer 1

The correct option is A

$8{\mathrm{\pi r}}^2$

Correct option: (a)$8{\mathrm{\pi r}}^2$

We know that,

$Areaofsemicircle=\frac{{\pi R}^2}{2}$ where $R$is the radius.

Then, the area of a semicircle of the radius $4r$ is

$\begin{array}{rcl}Areaofsemicircle& =& \frac{{\pi R}^2}{2}\\ & =& \frac{{\pi \left(4r\right)}^2}{2}\\ & =& \frac{\mathrm{\pi }\times 16{\mathrm{r}}^2}{2}\\ & =& 8{\mathrm{\pi r}}^2\end{array}$

Hence, the correct option is (a)