- #1
Noah1
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it is given that the perimeter of the rectangle is (80 + 120 + 80 + 120) = 400 cm From this you need to make a cylinder with maximin volume:
400 = 2r + 2h
2h = 400 - 2r
h = 200 - r .
We wish to MAXIMIZE the total VOLUME of the resulting CYLINDER
V = πr^2 h
However, before we differentiate the right-hand side, we will write it as a function of r only. Substitute for h getting
V = πr^2 h
V = πr^2 (200-r)
V = π(200r^2-r^3 )
Now differentiate this equation, getting
V’ = π(200r^2-r^3 )
V’ = π(400r-3r^2 )
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At this point I don't know where to go from here to solve for r
400 = 2r + 2h
2h = 400 - 2r
h = 200 - r .
We wish to MAXIMIZE the total VOLUME of the resulting CYLINDER
V = πr^2 h
However, before we differentiate the right-hand side, we will write it as a function of r only. Substitute for h getting
V = πr^2 h
V = πr^2 (200-r)
V = π(200r^2-r^3 )
Now differentiate this equation, getting
V’ = π(200r^2-r^3 )
V’ = π(400r-3r^2 )
- - - Updated - - -
Noah said:it is given that the perimeter of the rectangle is (80 + 120 + 80 + 120) = 400 cm From this you need to make a cylinder with maximin volume:
400 = 2r + 2h
2h = 400 - 2r
h = 200 - r .
We wish to MAXIMIZE the total VOLUME of the resulting CYLINDER
V = πr^2 h
However, before we differentiate the right-hand side, we will write it as a function of r only. Substitute for h getting
V = πr^2 h
V = πr^2 (200-r)
V = π(200r^2-r^3 )
Now differentiate this equation, getting
V’ = π(200r^2-r^3 )
V’ = π(400r-3r^2 )
At this point I don't know where to go from here to solve for r