How do you find the circumference when you ONLY know the area?

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19-02-2015
Mathematics

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How do you find the circumference when you ONLY know the area?

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AL2006 AL2006 · Answer 1 · 2015-02-19T21:23:41-05:00

It's easy if you remember the formulas you learned for the area, diameter,
and circumference of a circle:

-- Area = (pi) (radius)²
-- Diameter = (2) (radius)
-- Circumference = (pi) (diameter)

You know the area. So let's use the first formula to find the circle's radius.

Area = (pi) (radius)²

Divide each side by (pi): Area/pi = (radius)²

Radius = √(area/pi)

Now use the second formula to find the circle's diameter:

Diameter = (2) (radius)

Diameter = 2 √(area/pi)

Now use the third formula to find the circle's circumference:

Circumference = (pi) (diameter)

Circumference = (pi) (2) √(area/pi)

With just a little tweak, that can be written slightly more simply:

Circumference = 2 √(pi x area)

See ? Just the three circle formulas,and a lot of massaging.