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The dimensions of a closed rectangular box are measured as 50 centimeters, 90 centimeters, and 80 centimeters, respectively, with the error in each measurement at most .2 centimeters. Use differentials to estimate the maximum error in calculating the surface area of the box.

Verified Answer :

Need to get the total surface area of the box

L=length, W=Width, H=height

A = 2LW+2WH+2LH


Take derivative of that

dA=[2(dL)W+2L(dW)]+[2(dW)H+2W(dH)]+[2(dL)H+2L(dH)]

dA is your maximum error.


Since each side has same error its 0.2cm so therefore

dL=dW=dH=0.2cm

L=90cm

W=80cm

H=50cm

 
Just sub in the value in the above equation, and your resulting value will be your maximum error.

dA=[2(0.2)80+290(0.2)]+[2(0.2)50+280(0.2)]+[2(0.2)50+290(0.2)] 
dA=176