SOLUTION: Find the maximum volume of a cylinder if the sum of its height and radius is 60cm

Question 1048773: Find the maximum volume of a cylinder if the sum of its height and radius is 60cm
Found 2 solutions by solver91311, robertb:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If the sum of the height and the radius is 60, then the height as a function of the radius is . So the volume as a function of the radius is then:

Then

Which has a zero at

Since

equals when , is a local maximum of the original function.

John

My calculator said it, I believe it, that settles it

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
h+r = 60, and ===>
===> V' =
Letting V' = 0, we get r = 0, 40.
Eliminate r = 0. ===> Absolute extremum at r = 40.
Now V" = ===> V"(40) =
===> absolute maximum when r = 40.
===> h = 60 - 40 = 20 cm.
===> Maximum volume is cm^3.
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