Use differentials to estimate the amount of material in a closed cylindrical can

Question

Use differentials to estimate the amount of material in a closed cylindrical can that is 40 cm high and 16 cm in diameter if the metal in the top and bottom is 0.2 cm thick, and the metal in the sides is 0.05 cm thick. Note, you are approximating the volume of metal which makes up the can (i.e. melt the can into a blob and measure its volume), not the volume it encloses.
The differential for the volume is
dV= ? dr+ ? dh

(enter your answer in terms of r and h )
dr= ?and dh= ?

(be careful)
The approximate volume of material is ? cm3.

Explanation / Answer

dV= 40+16dh
dr= 0.2and dh=0.05-0.2(be careful)
The approximate volume of material is 418 cm^3

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