SOLUTION: A right cylinder is constructed such that the sum of its radius and twice its height is 18. What should the radius and height be in order to create a cylinder of maximum volume? Th

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Question 839438: A right cylinder is constructed such that the sum of its radius and twice its height is 18. What should the radius and height be in order to create a cylinder of maximum volume? The radius is represented by x.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A right cylinder is constructed such that the sum of its radius and twice its height is 18.
x + 2h = 18
2h = (18-x)
h = (9-.5x)
What should the radius and height be in order to create a cylinder of maximum volume?
The radius is represented by x.
:
V = pi%2Ax%5E2%2Ah
replace h with (9-.5x)
V = pi%2Ax%5E2%2A%289-.5x%29
graphically
+graph%28+300%2C+200%2C+-6%2C+30%2C+-200%2C+1500%2C+pi%2Ax%5E2%2A%289-.5x%29%29+
Max volume at x=12 is the radius
find the height
h = 9 - .5(12)
h = 3 is the height