Question

Find the exact area of a circle if its circumference is 36 cm.

Answer 1

The circumference of a circle of radius r is given by:

$C=2\pi r$

And the area of a circle with radius r is given by:

$A=\pi r^2$

We are told that the circumference of the circle is 36π cm which means that we can construct an equation for r:

$C=2\pi r=36\pi$

We can divide both sides by 2π:

$\begin{gathered} \frac{2\pi r}{2\pi}=\frac{36\pi}{2\pi} \\ r=18 \end{gathered}$

So the radius is 18cm. Then the area of the circle is given by:

$A=\pi\cdot18^2=324\pi$

So the answer is 324π cm².