Expert: Sherry Wallin - 7/21/2010

Question
express area of circle as function of its circumference

Answer
nisarg~
    The area of a circle is pi*r^2 and the circumference of a circle is 2*pi*r. What level of math are you doing? I ask this because if you take the first derivative of the area you will get the circumference.
Let f(x) = pi*r^2 then f'(x) = 2*pi*r
Another way to do this problem is to solve for the radius in the formula for circumference:
C = 2*pi*r
C/(2*pi) = r
now substitute this back into the formula for area of a circle:
A = pi*r^2
A = pi[C/(2*pi)]^2
A = pi*C^2/(2^2*pi^2)
A = pi*C^2/(4*pi^2)  you must square each factor so it is 2^2 * pi^2
A = C^2/(4*pi)   pi on top cancels with one of the pi's on bottom

Math Prof