SOLUTION: 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

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)

RELATED QUESTIONS
An open-topped cylindrical pot is to have volume 55 cm3. Determine the maximum possible... (answered by ikleyn)

An open-topped conical birthday hat is to have volume 55 cm3. Determine the minimum... (answered by ankor@dixie-net.com)

An open-topped cylindrical cup is to have volume 125 cm3. Determine the minimum possible... (answered by ankor@dixie-net.com)

Calculus Optimization A closed cylindrical can is to be constructed so that it has a... (answered by ikleyn)

A company wants to manufacture an open cylindrical bucket of volume 10 litres (10000... (answered by Skylarkerau)

A rectangular sheet of metal has dimensions of 60cm by 24cm. It is to be made into an... (answered by josgarithmetic)

A cylindrical metal container, open at the top, is to have a capacity of 24 cubic metres. (answered by greenestamps)

A box with a square base and open Top is to have a volume of 62.5 cm³. Neglect the... (answered by ikleyn)

This is a calculus problem. A cylindrical container is to hold 20π cm3. The bottom... (answered by Fombitz)