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Thread: Diect proportion

  1. October 31st 2008, 07:58 PM #1
    helloying
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    Diect proportion

    The price $p of a steel ball is proportional to the cube of its radius x cm It is known that the price is $48 for a teel ball of certain radius R cm. Find the price of a steel ball of radius R/2 cm . Ans is $6.

    Please explain to me how to solve why is it $6
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  2. October 31st 2008, 08:19 PM #2
    Chop Suey
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    Given:
    p = kr^3 for some constant k.

    48 = kR^3

    p = k\left(\frac{R}{2}\right)^3


    Now, let's rearrange the third equation:

    p = k\frac{R^3}{8} \implies 8P = kR^3

    Notice tha kR^3 from second equation equals 48, so substitute:

    8p = 48

    p = ...
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