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

Find the exact area of a circle if its circumference is 36 cm.-example-1
User LesterDove
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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.

User Shengy
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