Answer:
[tex]r=\sqrt{\frac{A}{\pi}}[/tex]
Step-by-step explanation:
Given:
The area 'A' of a circle with radius equal to 'r' is given as:
[tex]A=\pi r^2[/tex]
In order to rewrite the given formula in terms of radius 'r', we need to isolate 'r'.
Dividing both sides by π, we get:
[tex]\frac{A}{\pi}=\frac{\pi r^2}{\pi}[/tex]
As [tex]\frac{\pi}{\pi}=1[/tex], the above equation becomes:
[tex]r^2=\frac{A}{\pi}[/tex]
Taking square root both the sides, we get:
[tex]\sqrt{r^2}=\sqrt{\frac{A}{\pi}}\\r=\sqrt{\frac{A}{\pi}}[/tex]
We neglect the negative result while taking square root as the radius can't be a negative number.
Thus, the formula for radius 'r' in terms of area 'A' is given as:
[tex]r=\sqrt{\frac{A}{\pi}}[/tex]
