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} (2\pi r)/(2\pi)=(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.