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Answer:
The maximum error in calculating the surface area of the box is 72 square centimeters.
Step-by-step explanation:
From Geometry, the surface area of the closed rectangular box (), in square centimeters, is represented by the following formula:
(1)
Where:
- Width, in centimeters.
- Length, in centimeters.
- Height, in centimeters.
And the maximum error in calculating the surface area (), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:
(2)
Where:
- Measurement error in width, in centimeters.
- Measurement error in length, in centimeters.
- Measurement error in height, in centimeters.
If we know that ,
,
and
, then the maximum error in calculating the surface area is:
The maximum error in calculating the surface area of the box is 72 square centimeters.