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Thread: Elementary Algebra Help please

  1. #1
    Dec 2008

    Question Elementary Algebra Help please

    How so I figure out this equation? I am studing to go back to school and this is one of the questions I just dont remember how to do.

    I have a small circle inside a large circle with space inbetween them. Both circles have the same center, and the radius of the larger circle is R. if the radius of the smaller circle is 3 units less than R, which of the following represents the area of the shaded region (the space inbetween the small and big circle)

    answer is: pie signRpower of 2 - pie sign(R-3)power of 2

    if you can understand that - please help me do the same. how did that get that and why is it written like that?
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  2. #2
    Super Member Aryth's Avatar
    Feb 2007
    Well, when you have a shape inside of a shape, the area of the region outside of the inner shape is almost always:

    $\displaystyle A_{shaded} = A_{outer} - A_{inner}$

    So, we know that:

    $\displaystyle Radius_{outer} = R$

    $\displaystyle Radius_{inner} = R - 3$

    We also know that the area of a circle is:

    $\displaystyle A = \pi r^2$

    So, therefore:

    $\displaystyle A_{outer} = \pi R^2$

    $\displaystyle A_{inner} = \pi (R - 3)^2$

    And we get:

    $\displaystyle A_{shaded} = A_{outer} - A_{inner} = (\pi R^2) - [\pi (R - 3)^2]$

    Basically, say you have a paper circle of radius R, and you cut out a smaller circle of radius R - 3, you are left with the shaded region you described. It therefore makes sense that all you do is take the area of the larger circle and subtract, or take away, the area of the smaller circle to get the desired area.

    Hopefully this helps.
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  3. #3
    Dec 2008

    Talking thanks for the help.

    thanks for your help. That made sense once I read it. I just had to be reminded. Thanks for that help ALOT. Appreciate it.
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