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 50 cm high and 20 cm in diameter if the metal in the top and bottom is 0.1 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 therms of r and h )
dr= __________ and dh= ___________ (be careful)
The approximate volume of material is____________ cm^3   .

Explanation / Answer

v=pi*r^2*h

dv=pi*2*r*h*dr+ pi*r^2*dh

use h=0.5 m
r=0.1 m
dr=0001 m
dh=0.0005 m

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