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Math Help - more sphere help on ratios

  1. #1
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    more sphere help on ratios

    sphere 1 has a surface area of A_1
    and has a volume of V_1
    sphere 2 has a surface area of A_2
    and has a volume of V_2
    if the radius of sphere 2 is 3 times greater than the radius of sphere 1,
    what is the ratio A_1/A_2 of the surface areas?
    what is the ration V_1/V_2 of the volumes?

    _ means that the number is underscored like this -->A_1
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  2. #2
    Senior Member eumyang's Avatar
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    Let r be the radius of sphere 1. Then the radius of sphere 2 is 3r. The surface area of sphere 2 is
    SA_2 = 4 \pi (3r)^2 = 36 \pi r^2

    Since the surface area of sphere 1 is
    SA_1 = 4 \pi r^2,

    the ratio SA1/SA2 would be
    \dfrac{SA_1}{SA_2} = \dfrac{4\pi r^2}{36\pi r^2} = \dfrac{1}{9}.

    Now, you do the same thing with the volume. Remember that
    V = \frac{4}{3}\pi r^3.
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  3. #3
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    ok so in volume
    V_1= 4/3(pi)r^2
    V_2=12(pi)r^2

    so the ration would be:

    v_1/v_2=4/3(pi)r^2/12(pi)r^2=1/9

    ^is this correct?
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  4. #4
    Senior Member eumyang's Avatar
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    The formula you used for volume is not right. It's
    V = \frac{4}{3}\pi r^{\bold{3}}. The r is cubed, not squared. Can you try again?
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  5. #5
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    v_1/v_2=4/3(pi)r^3/36(pi)r^3=1/27
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  6. #6
    Senior Member eumyang's Avatar
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    Yep, that's right!
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