# How do you use differentials to estimate the maximum error in calculating the surface area of the box if the dimensions of a closed rectangular box are measured as 60 centimeters, 80 centimeters, and 90 centimeters, respectively, with the error in each measurement at most .2 centimeters?

##### 1 Answer

Mar 9, 2015

The answer is

The surface area of a closed rectangular box is

where

The differential of area is used as the approximate maximum error.

Each measurement has same maximum error, all of the differentials are the same. Namely,

Substituting into:

gives: