SOLUTION: an open topcylindrical container has a volume of 100 pie. construct a single-variable object function suited to minimizing the surface area?

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Question 607004: an open topcylindrical container has a volume of 100 pie. construct a single-variable object function suited to minimizing the surface area?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
an open top cylindrical container has a volume of 100 pie.
construct a single-variable object function suited to minimizing the surface area?
:
x = the radius
The volume of a cylinder: V = pi%2Ax%5E2%2Ah
pi%2Ax%5E2%2Ah = 100pi
divide both side by pi
x^2*h = 100
h = 100%2Fx%5E2
:
The surface area of a open topped cylinder: S.A. = 2%2Api%2Ar%2Ah + pi%2Ar%5E2
replace h with
S.A. = 2%2Api%2Ax%2A%28100%2Fx%5E2%29 + pi%2Ax%5E2
Cancel x
S.A. = 2%2Api%2A%28100%2Fx%29 + pi%2Ax%5E2
:
Graph this equation; y = surface area

Looks like minimum surface area occurs when x=4.64 (radius), height = 4.64 also (100/4.64^2)
S.A. ~ 200 sq/units