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Math Help - Linearization Word Problem?

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    Linearization Word Problem?

    The edge of a cube is measured as 10 cm with an error of 1%. The cube's volume is to be calculated from this measurement. Estimate the percentage error in the volume calculation.


    Please explain to me how to do this.
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    Quote Originally Posted by Seigi View Post
    The edge of a cube is measured as 10 cm with an error of 1%. The cube's volume is to be calculated from this measurement. Estimate the percentage error in the volume calculation.


    Please explain to me how to do this.
    The volume of a cube is

    V=s^3

    The error is \frac{\Delta V}{V} \approx \frac{dV}{V}

    We know that s=10cm \mbox{ and } \Delta s =.01(10cm)=0.1cm

    dV =3s^2ds

    using the above formula we get

    \frac{3(10cm)^2(0.1cm)}{(10cm)^3}=\frac{30cm^3}{10  00cm^3}=\frac{3}{100}=3\%
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