Finding circumference of a circle given its area

Question

So, I'm learning mathematics from the beginning & currently I'm learning basic geometry from Khan Academy.

I'm trying to find the circumference of a circle when its area is 9π units, by applying formula I learnt in this video: https://m.youtube.com/watch?v=-jqWW22FMdI

I found that if area of circle is 9π units its circumference must be 6π.

Here's what I did:

https://i.stack.imgur.com/TYTUI.jpg

Is my calculation right or wrong?

Answer 1

$$a=\pi r^2,c=2\pi r\to c=\sqrt{4\pi^2r^2}=\sqrt{4\pi a}$$

and

$$\sqrt{4\pi\cdot9\pi}=6\pi.$$

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Also

$$a=\frac{c^2}{4\pi}$$ and $$r=\sqrt{\frac a\pi}=\frac c{2\pi}.$$

Answer 2

$circumference^2 = 4×\pi×area$