Pre-cal question!! if ur smart only!?

Question

Express the area (A) of a circle as a function of its circumference(C)? well, i looked at the back and the answer was A= C squared/4pi!!! Dont know the steps!!

Answer 1

Okay, you know that:

A=πr²

and:

C=2πr

so obviously:

r=C/(2π)

Now just substitute this into the forumla for area:

A=π(C/(2π))²

And simplify:

A=π(C²/(2²π²)=C²/(4π)

Answer 2

area = pi * r ^ 2
Circumference = 2 * pi * r
r = c / 2pi
area = pi * (c/2pi) ^ 2
area = pi * (c^2 / 4pi^2)
area = c^2 / 4 pi