How do you find the circumference of a circle from the area?

Answer 1

That's a nice little algebra exercise.

Before you can begin, you need to know the formulas for the

circumference and area of a circle:

-- Circumference = (pi) x (diameter)

-- Area = (pi) x (radius)2

-- It will also be very helpful to know that the radius is 1/2 of the diameter.

And now you're ready to begin. What I'll do is solve the area formula for the radius,

adjust that to equal the diameter, and substitute that into the circumference formula.

Fasten your seat belt if necessary.

Area = (pi) x (radius)2

Divide each side by (pi):

(radius)2 = area/pi

Take the square root of each side:

Radius = sqrt (area/pi)

Double each side:

2 x radius = 2 sqrt(area/pi)

Now go and get the formula for the circumference:

Circumference = (pi) x (diameter)

Do you have the diameter ? Look a few lines higher ... you just found (2 x radius),

and that's the diameter. Substitute it in the circumference formula:

Circumference = (pi) x 2 x sqrt(area/pi) .

That's it. If you know the area, then you know everything on the right side,

and you can calculate the circumference.

The result can be tidied up a bit, without changing it:

Circumference = 2 x sqrt( area x pi )