The Area Of A Circle Is 32pi. What Is The Circumference?


2 Answers

Anonymous Profile
Anonymous answered
Area of a circle is Pi * radius2
The circumference of a circle is 2 * Pi * radius

C = 2 Pi r

You already know the area; 
A = Pi r2
   = 32 Pi

so the radius is the square root of 32.  Substitute sqrt(32) into 2 Pi r to get the circumference;

C = 2 Pi sqrt(32)

   = 2 Pi 4 sqrt(2)

   = 8 sqrt(2) Pi

   = ~ 35.5
Oddman Profile
Oddman answered
The area of a circle is
area = Pi*r2

The circumference is
circumference = 2*Pi*r

We can solve the area equation and put the result in the circumference equation in order to determine the circumference as a function of the area.

area = Pi*r2
area/Pi = r2
√(area/Pi) = r
circumference = 2*Pi*r = 2*Pi*√(area/Pi)

Plugging in the numbers, we have
circumference = 2*Pi*√(32*Pi/Pi) = 2*Pi*√32
circumference = 8*Pi*√2
thanked the writer.
Anonymous commented
A minor note, the area equations need superscript 2's or a caret sign ^2. But what is important is the answer is accurate.
Oddman commented
Correct. I sometimes find it interrupts my train of thought to have to select the superscript button each time. Then I forget to go back and fix it, or neglect to find all of the places that need fixing. Thank you for your comment. I hope it works now.

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