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.

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.       Log On


   

Question 843139: 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.

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
JUST the tubular surface, no top or bottom disk:

h for height, r for radius,
%282%2Api%2Ar%29%28h%29 is the surface area, and r=2h.
Surface Area is then highlight_green%282%2Api%282h%29%28h%29%29.

The volume: h%2Api%2Ar%5E2=164
h%2Api%2A%282h%29%5E2=164
4%2Api%2Ah%5E3=164
h%5E3=164%2F%284%2Api%29
h%5E3=41%2Fpi
h=root%283%2C41%2Fpi%29-----useful for the "height"

Use the value for h as it is in the surface area formula shown green highlighted.
Surface Area:
Either way you can finish the computation using a calculator or some other reasonable approximation.