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Math Help - Volume

  1. #1
    Junior Member Dragon's Avatar
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    Volume

    Suppose that eh volume of a ball is equal to Pie/6 times the volume of a cube What is the ration of the surface area of the ball to that of the cube?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Dragon View Post
    Suppose that eh volume of a ball is equal to Pie/6 times the volume of a cube What is the ration of the surface area of the ball to that of the cube?
    I must be in a crabby mood tonight.

    Pet peeve warning!!

    It's spelled "pi" not "pie."

    Pet peeve over.

    Okay. We know that V_b = \frac{ \pi }{6} \cdot V_c.

    We also know that
    V_b = \frac{4}{3} \pi r^3
    V_c = s^3
    S_b = 4 \pi r^2
    S_c = 6s^2
    (Where "s" is the side of the cube.)

    So, solve V_b for r:

    r = \left ( \frac{3}{4 \pi}V_b \right ) ^{1/3}

    So
    S_b = 4 \pi \left ( \frac{3}{4 \pi}V_b \right ) ^{2/3}

    Sim: S_c = 6 \left ( V_c \right ) ^{2/3}

    Now sub in the relation for V_b into the S_b equation and take the ratio.

    -Dan
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