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 60 cm high and 24 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 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=

dh=____________ (be careful)
The approximate volume of material is ______________cm3.

Explanation / Answer

volume v=pir^2 h

dv=2pirh dr+pir^2 dh

dr=0.1 ,dh=2*0.1 =0.2 ,h=60,r=24/2=12

The approximate volume of material=dv=pi*((2*12*60*0.1)+(12*12*0.2))= 543 cm^3

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.