SOLUTION: Given that the volume of a cylinder is 164, and the radius of the cylinder is twice the height, find the surface Area of the cylinder. I tried r=7.227 to get pi(7.227)^2 to ge

Algebra ->  Surface-area -> SOLUTION: Given that the volume of a cylinder is 164, and the radius of the cylinder is twice the height, find the surface Area of the cylinder. I tried r=7.227 to get pi(7.227)^2 to ge      Log On


   

Question 842348: Given that the volume of a cylinder is 164, and the radius of the cylinder is twice the height, find the surface Area of the cylinder.
I tried r=7.227 to get pi(7.227)^2 to get 164 but that did not work.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
This analysis assumes just the wall cylinder without any top or bottom.

r=2h, r is radius and h is height or tallness.
Volume is h%2Api%2Ar%5E2=164
%28r%2F2%29pi%2Ar%5E2=164
%281%2F2%29pi%2Ar%5E3=164
pi%2Ar%5E3=328
r=root%283%2C328%2Fpi%29
highlight%28r=2%2Aroot%283%2C41%2Fpi%29%29
This means highlight%28h=root%283%2C41%2Fpi%29%29

The surface area of just the tube part without any top or bottom:
%282%2Api%2Ar%29%2Ah which is circumference by "length".
Substitute the values found.
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Those Substitutions:
2%2Api%2A%282%2Aroot%283%2C41%2Fpi%29%29%28root%283%2C41%2Fpi%29%29
highlight%284%2Api%28root%283%2C41%2Fpi%29%29%28root%283%2C41%2Fpi%29%29%29
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A separate substep, root%283%2C41%2Fpi%29=root%283%2C13.050705%29=highlight_green%282.3544%29
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Surface area may be represented 4%2Api%2A2.3544%2A2.3544
4%2Api%2A5.54314...
highlight%2822.1725%2Api%29