The dimensions of a closed rectangular box are measured as 78 cm, 52 cm, and 39 cm, 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.

Question

anonymous · Answer

With a .2cm margin of error, we can calculate the area of the possible error. Imagine a cube that would either be extra, or short of the actual box. The area of this cube is between 0 and .2 cubed.
So we can find the maximum of this cube (being .2 cubed) as .008 cm(cubed)