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Check work on finding max error of Surface Area

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    The dimensions of a closed rectangular box are measured as 80cm, 60cm, and 50cm,respectively,
    with a possible error of 0.2cm in each dimension. Use differentials to estimate the maximum error
    in calculating the surface area of the box


    3. The attempt at a solution

    I figured out that the surface area of a closed rectangular box is this :

    SA = 2[ xy + yz + xz]

    so, differentiating with respect to x,y and z I get :

    d[SA] = 2[ yzD_x + xzD_y + xyD_y]

    inserting value,
    x = 80
    y = 60
    z = 50
    dx = dy = dz = 0.2 ; since this is where the max error will occur I get

    d[SA] = 152cm^2

    which is about 0.06% error.

    Is this correct?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 18, 2009 #2

    Mark44

    Staff: Mentor

    That's what I get.
     
  4. Oct 18, 2009 #3
    Thanks
     
  5. Oct 18, 2009 #4
    Ummm...i plugged in The numbers for this, and my answer is too big (4720) when x=80,y=60,z=50, and the d's being 0.2 exactly how were the numbers plugged in? There is a step i'm missing.
     
  6. Oct 19, 2009 #5

    Mark44

    Staff: Mentor

    What formula did you use? Both the OP and I got exactly the same result with the formula he posted.
     
  7. Oct 19, 2009 #6
    Is your answer 0.06% derived from 152/23600?
     
  8. Oct 26, 2011 #7
    0.2((2y+2z)+(2x+2z)+(2y+2x))

    where
    (2y+2z) is the partial derivative of SA with respect to x
    (2x+2z) is the partial derivative of SA with respect to y
    (2y+2x) is the partial derivative of SA with respect to z
     
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