Question

If the area of a circle is $\pi {\text{m}}^2,$ then its:

• A. $\text{radius = 1 m}$
• B. $\text{diameter = 1 m}$
• C. $\text{perimeter =}\pi \text{m}$
• D. $\text{perimeter =}2\pi \text{m}$

Answer 1

Answer: (A), (D)

$\text{perimeter =}2\pi \text{m}$

Given, the area of the circle is $\pi {\text{m}}^2.$

The area of the circle is given by $A=\pi r^2,$ where $r$ is the radius of the circle.
$\therefore \pi r^2=\pi$
Divide both sides by $\pi$
$\Rightarrow \frac{\pi r^2}{\pi }=\frac{\pi }{\pi }$
$\Rightarrow r^2=1$
Taking square root both sides
$\Rightarrow \sqrt{r^2}=\sqrt{1}$
$\Rightarrow r=\pm 1$
$\Rightarrow r=1$ m
$(\because \text{The radius of a circle cannot be negative}$
$\therefore r=-1\text{is rejected})$

We know that, the diameter of the circle$\left(d\right)$ is twice its radius$\left(r\right).$
$d=2\times r$
$=2\times 1\text{m}=2\text{m}$

$\text{Perimeter of the circle}=2\pi r=2\times \pi \times 1=2\pi \text{m}$

Hence, options (a) and (d) are correct choices.