Question

Find the diameter of a circle if its area is $49\pi {\text{cm}}^2.$
cm

Answer 1

Given, the area of the circle is $49\pi {\text{cm}}^2.$

The area of the circle is given by $A=\pi r^2,$ where $r$ is the radius of the circle.
$\therefore \pi r^2=49\pi$
Divide both sides by $\pi$
$\Rightarrow \frac{\pi r^2}{\pi }=\frac{49\pi }{\pi }$
$\Rightarrow r^2=49$
Taking square root both sides
$\Rightarrow \sqrt{r^2}=\sqrt{49}$
$\Rightarrow r=\pm \sqrt{7\times 7}$
$\Rightarrow r=\pm 7$
$\Rightarrow r=7$ cm
$(\because \text{The radius of a circle cannot be negative}$
$\therefore r=-7\text{is rejected})$

We know that, the diameter of the circle$\left(d\right)$ is twice its radius$\left(r\right).$
$d=2\times r$
$=2\times 7$ cm
$=14$ cm

Hence, the diameter of the given circle is $14$ cm.