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Variation and Changing factors help

  1. Oct 24, 2007 #1
    1. The problem statement, all variables and given/known data
    "If the circumference of a circle changes by a factor of 3, then its area changes by a factor of ____."

    2. Relevant equations

    3. 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.
    Last edited: Oct 24, 2007
  2. jcsd
  3. Oct 24, 2007 #2
    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.
  4. Oct 24, 2007 #3


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    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.
  5. Oct 24, 2007 #4
    Okay, thanks alot both of you. I appreciate it.
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