If circle circumference changes by factor of 3, how does area change?

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AKahan
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Homework Statement


"If the circumference of a circle changes by a factor of 3, then its area changes by a factor of ____."

Homework Equations


C=2*Pi*r
A=Pi*r^2

The Attempt at a Solution


I really don't know where to start.Recently I have been learning about the changing of factors and I'm having trouble. I do not understand where to start my problem and/or plug in numbers.If someone could give me a head start or a hint at how to approach this problem that would be great because I have many problems like this that I need to complete. Thanks.
 
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Well the only thing that can change is r because it is not a constant like Pi or 2.

Hope that helps.
 
AKahan said:

Homework Statement


"If the circumference of a circle changes by a factor of 3, then its area changes by a factor of ____."

Homework Equations


C=2*Pi*r
A=Pi*r^2

The Attempt at a Solution


I really don't know where to start.


Recently I have been learning about the changing of factors and I'm having trouble. I do not understand where to start my problem and/or plug in numbers.If someone could give me a head start or a hint at how to approach this problem that would be great because I have many problems like this that I need to complete. Thanks.

Consider the situation before you changed anything. Call the initial radius [itex]r_{old}[/itex] Then the "old' circumference and area are

[tex]C_{old} = 2 \pi r_{old}[/tex] and [tex]A_{old} = \pi r_{old}^2[/tex]

Now after you made the chaneg, write everything in terms of the new radius:
[tex]C_{new} = 2 \pi r_{new}[/tex] and [tex]A_{new} = \pi r_{new}^2[/tex]

Your goal is to find the ratio [itex]\frac{A_{new}}{A_{old}}[/itex] .Obviously, this is simply (from the above formula)

[tex]\frac{A_{new}}{A_{old}} = \frac{r_{new}^2}{r_{old}^2}[/tex]

Now, use the information provided that [itex]C_{new} = 3 C_{old}[/itex]. From this and the equations given above, you can figure out what [itex]r_{new}[/itex] is in terms of [itex]r_{old}[/itex], right? In other words, find the ratio [itex]\frac{r_{new}}{r_{old}}[/itex] . Then plug it back in the above equation.
 
Okay, thanks a lot both of you. I appreciate it.