Thread: Differential word problem

1. 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.

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

The surface area of the box is:

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

Take differentials:

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

Substitute values from [1]:

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

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

3. Thanks alot!!