An equation for the area as a function of circumfrence?

Question

A=2(pi)(r^2)?

Answer 1

First, your formula for the area of a circle is not correct.

A = pi(r^2)

Somehow you got a 2 in there which occurs in C=2(pi)r.

You want to take the formula for area which you can use when you know the radius, and turn it into a formula for area you can use whenyou know the circumference. That should be easy we know that

C = 2(pi)r

Let's solve this for r by dividing both sides by 2pi to get

r = C/2pi which we can substitute for r in the area

formula to get A = pi(r^2) = pi(C/2pi)^2. A factor of pi canceles to give

A = C^2/4pi

Answer 2

An equation for the area as a function of circumfrence?

Speaking of circumference, you probably mean the circumference of a circle, which is 2*pi*r.

For finding the circumference by using area as the function?

Well, if you set the equation as f(r) for r = radius;

f(r)= pi*r^2.

then the change for radius will get you,

f'(r) = 2*pi*r dr/dt

So the function is f(r)= pi*r^2.

Answer: f(r)= pi*r^2.

Answer 3

A = π r²
C = 2 π r

Solve the circumference equation for r as a function of C:
r = C / 2π

Plug that r into the equation for area:
A = pi * (C/2π)²
A = pi * C² / 4π²
A = C² / 4π

Now area (A) is a function of circumference (C).

Answer 4

A= pi*r^2

C= 2(pi)r

You want A in terms of C. so, in the second equation, solve for r in terms of C, and substitute that value for r into the first equation.

Answer 5

C = 2piR so R = C/2pi

A = piR^2 so by substitution
A = pi(C/2pi)^2
A = pi ( C^2/4pi^2)
A = C^2/4pi or using functional notation
f(C) = C^2/4pi