SOLUTION: I am not sure were this question belongs but I need an algebraic expression that give the area of a circle witha circumfernce c. Here is the kicker I can't have any equal signs (=

Algebra ->  Equations -> SOLUTION: I am not sure were this question belongs but I need an algebraic expression that give the area of a circle witha circumfernce c. Here is the kicker I can't have any equal signs (=      Log On


   

Question 11821: I am not sure were this question belongs but I need an algebraic expression that give the area of a circle witha circumfernce c. Here is the kicker I can't have any equal signs (=) or have diameter (d) in any part of the answer.
The only hint I have to go off of is Hint: The circumference of a circle with radius r is 2*pi*r, and its area is pi*r^2.
Found 2 solutions by rapaljer, Earlsdon:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
C=+2%2Api%2Ar and A=+pi%2Ar%5E2

You want a formula for the Area in terms of the Circumference C.

So, solve for r in the first equation, by dividing both sides by 2%2Api.
C%2F%282%2Api%29+=+%282%2Api%2A+r%29%2F%282%2Api%29
r=+C%2F%282%2Api%29

Substitute this into the second formula, and you will have:
A+=+pi+%2A+r%5E2
A+=+pi+%2A+%28C%2F%282%2Api%29%29%5E2
A+=+pi+%2A+%28C%5E2%29%2F+%284%2Api%5E2%29

Divide out the pi factor
A+=+%28C%5E2%29+%2F%284%2Api%29+

I suppose without any equal signs the final answer is this: %28C%5E2%29%2F%284%2Api%29

R^2 at SCC

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, since you have been asked for an "expression", there wouldn'tbe any = signs any because "expressions" don't have = signs.
Let's write an expression for the area of a circle:
%28pi%29r%5E2 But you need it in terms of c, the circumference.
Let's write an equation for c:
c+=+2%28pi%29r Now, solve this for r:
r+=+c%2F2%28pi%29 and, after squaring, substitute this into the expression for the area:
%28pi%29%28c%5E2%2F4%28pi%29%5E2%29 Now simplify:
c%5E2%2F4%28pi%29 This is an expression for the area of a circle in terms of the circumference, c.