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Question 1189138: An open-topped cylindrical pot is to have volume 55 cm3. Determine the minimum possible amount of material used in making this pot? Show your complete solution
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The area is πr^2+2πrh
so πr(r+2h)=A
V=πr^2h=55,
so h=55/πr^2=17.507/r^2
A=πr(r+(110/πr^2))=πr^2+(110/r)
take the derivative, and set that equal to 0.
2πr-110/r^2=0
multiply through by r^2 and move the second term to the right
2πr^3=110
πr^3=55
r^3=17.507
r=2.60 cm
h=17.507cm^3/(2.60 cm)^2
=2.60 cm
So the total surface area is πr(r+2h)=2.60π(7.80), with units cm*cm or cm^2=63.54 cm^2 (rounding at end)
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