SOLUTION: A closed cylinder has total surface area equal to 600π. Show that the volume, V cm^3, of this cylinder is given by the formula V=300πr-πr^3, where r cm is the radius

Algebra ->  Surface-area -> SOLUTION: A closed cylinder has total surface area equal to 600π. Show that the volume, V cm^3, of this cylinder is given by the formula V=300πr-πr^3, where r cm is the radius      Log On


   

Question 1074738: A closed cylinder has total surface area equal to 600π. Show that the volume, V cm^3, of this cylinder is given by the formula V=300πr-πr^3, where r cm is the radius of the cylinder. Find the maximum volume of such a cylinder.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Total Surface area
Includes a length between the two circle parts, h.
2%2Api%2Ar%5E2%2Bh%2A2pi%2Ar=600pi
2pi%28r%5E2%2Bh%2Ar%29=600pi
r%5E2%2Bhr=300
hr=300-r%5E2
h=%28300-r%5E2%29%2Fr



VOLUME
h%2Api%2Ar%5E2
%28%28300-r%5E2%29%2Fr%29pi%2Ar%5E2
%28300%2Fr-r%29%28pi%2Ar%5E2%29
300pi%2Ar-pi%2Ar%5E3-------DONE


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Maybe you can do the rest - finding maximum volume