Question

Find the radius of a circular table if its area is $81\pi {\text{cm}}^2.$

• A. $3$ cm
• B. $6$ cm
• C. $12$ cm
• D. $9$ cm

Answer 1

The correct option is D $9$ cm

Given, the area of the circular table is $81\pi {\text{cm}}^2.$

The area of the circle is given by $A=\pi r^2,$ where $r$ is the radius of the circular table.
$\therefore \pi r^2=81\pi$
Divide both sides by $\pi$
$\Rightarrow \frac{\pi r^2}{\pi }=\frac{81\pi }{\pi }$
$\Rightarrow r^2=81$
Taking square root both sides
$\Rightarrow \sqrt{r^2}=\sqrt{81}$
$\Rightarrow r=\pm \sqrt{9\times 9}$
$\Rightarrow r=\pm 9$
$\Rightarrow r=9$ cm
$(\because \text{The radius of a round table cannot be negative}$
$\therefore r=-9\text{is rejected})$

Hence, radius of the given circular table is $9$ cm.
Option (d.) is the correct choice.