SOLUTION: An open-topped cylindrical cup is to have volume 125 cm3. Determine the minimum possible amount of material used in making this pot? Neglect the thickness of the material as well a

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Question 1189137: An open-topped cylindrical cup is to have volume 125 cm3. Determine the minimum possible amount of material used in making this pot? Neglect the thickness of the material as well as possible wastage. Give your answer accurate to 2 decimal places.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An open-topped cylindrical cup is to have volume 125 cm3.
pi%2Ar%5E2%2Ah = 125
h = 125%2F%28pi%2Ar%5E2%29
:
Determine the minimum possible amount of material used in making this pot?
A = the area of the material required
A = %28pi%2Ar%5E2%29%2B%282pi%2Ar%2Ah%29
A = pi%2Ar%28r%2B2h%29
replace h with 125%2F%28pi%2Ar%5E2%29
A = pi%2Ar%28r%2B2%28125%2F%28pi%2Ar%5E2%29%29%29
A = pi%2Ar%28r%2B%28250%2F%28pi%2Ar%5E2%29%29%29
A = %28pi%2Ar%5E2%29+%2B+%28250%2Fr%29
Graphically, radius on the x axis, area on y axis
+graph%28+300%2C+200%2C+-4%2C+8%2C+-100%2C+200%2C+%28pi%2Ax%5E2%29%2B%28250%2Fx%29%29+
minimum area when radius = 3.5 cm
Find the height
h = 125%2F%28pi%2A3.5%5E2%29
h = 3.25 cm is the height for minimum area
:
:
Check, find the volume using these dimensions
V = pi%2A3.5%5E2%2A3.25
V = 125.07 ~ 12