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Math Help - Differential word problem

  1. #1
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    Differential word problem

    Can someone help me with this one?


    The dimensions of a closed rectangular box are measured as 80cm, 60cm, and 50cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.


    I'm a bit clueless as to how to do this one.
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  2. #2
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    Hello, JonathanEyoon!

    The dimensions of a closed rectangular box are measured as 80cm, 60cm, and 50cm, resp.
    with a possible error of 0.2 cm in each dimension.
    Use differentials to estimate the maximum error in calculating the surface area of the box.

    We are given: . \begin{array}{ccc}L \:=\:80 && dL \:=\:0.2 \\ W \:=\:60 & & dW\:=\:0.2 \\ H \:=\:50 && dH \:=\:0.2 \end{array} .[1]


    The surface area of the box is:

    . . A \;=\;2LW + 2WH + 2LH


    Take differentials:

    . . dA \;=\;2L\!\cdot\!dW + 2W\!\cdot\!dL + 2W\!\cdot\!dH  + 2H\!\cdot\!dW + 2L\!\cdot\!dH + 2H\!\cdot\!dL


    Substitute values from [1]:

    . . dA \;=\;2(80)(0,2) + 2(60)(0.2) + 2(60)(0.2) + 2(50)(0.2) + 2(80)(0.2) + 2(50)(0.2)

    . . dA \;=\;32 + 24 + 24 + 20 + 32 + 20 \;=\;\boxed{152}

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  3. #3
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    Thanks alot!!
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