Answer
Quadratic equation $\pi r^2=90$.
r=$5.4\;cm$.
Work Step by Step
Let the radius of the circle be $=r$.
Area of the circle $=\pi r^2$.
Given area of the circle $=90\;cm^2$.
Equate both areas.
$\Rightarrow \pi r^2=90$
Divide both sides by $\pi$.
$\Rightarrow \frac{\pi r^2}{\pi}=\frac{90}{\pi}$
Simplify.
$\Rightarrow r^2=\frac{90}{\pi}$
Take the square root on both sides.
$\Rightarrow \sqrt{ r^2}=\pm\sqrt{\frac{90}{\pi}}$
Simplify.
$\Rightarrow r=\pm5.4\;$
The area cannot have a negative sign.
Hence, the radius of the circle is $5.4\;cm$.
