How do you find the exact circumference of a circle using the area?

Answer 1

Most people know the following two equations for a circle:

c = 2πr

a = πr2

What you can do then, is rearrange the latter of the two, solving for r, and then plug it into the first one where r currently is:

a = πr2

r2 = a/π

r = (a/π)1/2

Now that we have an equation for radius with respect to area, we can simply plug that into our equation for circumference:

c = 2πr

c = 2π(a/π)1/2

c = 2(π2)1/2(a/π)1/2

c = 2(π2a/π)1/2

c = 2(πa)1/2

Giving us the final answer. The circumference of a circle is equal to twice the square root of the product of pi and it's area.