Question

the maximum volume of the cylinder is
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Answer 1

Answer:

Therefore the volume is a maximum when 2r−2h+h=0, so h=2r and hr=2. Let the ratio of height to radius be ρ, then h=ρr. The volume of the cylinder is V=πr2h=πρr3. Let k=h/r, where h is the height and r is the radius.

Step-by-step explanation:

1 Answer

Set-Up (find the function to optimize) For a cylinder the volume is V=πr2h.

And for a cylinder with no top, the surface area is A=πr2+2πrh.

Given the area is 3π , we can express the volume using one variable instead of two. A=πr2+2πrh=3π .