1 Answer

Shengy · Answer 1 · 2023-02-13T06:01:40+0000

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.

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