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Math Help - Linearization Word Problem need help again

  1. #1
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    Linearization Word Problem need help again

    A manufacturer contracts to mint coins for the federal government. How much variation dr in the radius of the coins can be tolerated if the coins are to weigh within 1/1000 of their deal weight? Assume the thickness does not vary.
    I do not know where to began with this problem, i'm not good at word problem.
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  2. #2
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    Quote Originally Posted by Seigi View Post
    I do not know where to began with this problem, i'm not good at word problem.
    Let r denote the radius of the coin and h its thickness which is considered to be constant.
    The weight of the coin is proportional to its volume.

    Let dy denote the difference of 2 radii. Then you know that

    \dfrac{dy}{dr}=V'(r)=2\pi\cdot h \cdot r

    The maximum value of dy=\dfrac1{1000}V

    Therefore:

    2\pi \cdot h \cdot r \cdot dr=\dfrac1{1000}V  = \dfrac1{1000}\cdot \pi\cdot h \cdot r^2

    Solve for dr:

    dr=\dfrac{ \dfrac1{1000}\cdot \pi\cdot h \cdot r^2}{2\pi \cdot h \cdot r} = \dfrac1{2000} r
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