Variation and Changing factors help

[AKahan]

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.

 

[pooface]

Welcome to physics forums!

Well the only thing that can change is r because it is not a constant like Pi or 2.

Hope that helps.

 

[nrqed]

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 $r_{old}$ Then the "old' circumference and area are

$$C_{old} = 2 \pi r_{old}$$ and $$A_{old} = \pi r_{old}^2$$

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

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

$$\frac{A_{new}}{A_{old}} = \frac{r_{new}^2}{r_{old}^2}$$

Now, use the information provided that $C_{new} = 3 C_{old}$. From this and the equations given above, you can figure out what $r_{new}$ is in terms of $r_{old}$, right? In other words, find the ratio $\frac{r_{new}}{r_{old}}$ . Then plug it back in the above equation.

 

[AKahan]

Okay, thanks a lot both of you. I appreciate it.