Use differentials to estimate the amount of tin in a closed tin can with...?

Question

Use differentials to estimate the amount of tin in a closed tin can with diameter 6 cm and height 12 cm if the tin is 0.012 cm thick.

Please show ALL work.
Correct answer is 3.39 cm^3.

I need to know how to ARRIVE at the answer.

Answer 1

You get the exact answer as follows:

The area of the top and bottom is known. So is their thickness. So calculate, and don't forget to count them twice (once each for top and bottom. (Note -- they are very flat cylinders, so the volume is just pi r^2 h).

Then the height of the remaining cylindrical shell is known, namely 12 - 2*.012 cm.

The radius of the shell is the volume of a cylinder with radius 6 minus the volume of a cylinder with radius 6 - .012.

My guess, however, is that they don't want the precise answer, but rather the incorrect answer that comes from saying the volume of the can is approximately the volume of a cylinder with height 12 and diameter 6 minus the volume of a cylinder with height 12 -2*.012 and diameter 6*.012.