SOLUTION: A cylinder's height equals the diameter of its base. What fraction of the total surface area of the cylinder is the area of the two bases? Express your answer as a common fraction.

Algebra ->  Surface-area -> SOLUTION: A cylinder's height equals the diameter of its base. What fraction of the total surface area of the cylinder is the area of the two bases? Express your answer as a common fraction.      Log On


   

Question 947777: A cylinder's height equals the diameter of its base. What fraction of the total surface area of the cylinder is the area of the two bases? Express your answer as a common fraction.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
radius=k/2;
height=k;



Total Surface Area: 2%28%28pi%29%28k%2F2%29%5E2%29%2B2%2Api%2A%28k%2F2%29%2Ak
Simplify:
highlight_green%28%28pi%29%28%28k%5E2%29%2F2%2Bk%5E2%29%29

Just the top & bottom Surface Area: 2%28pi%2A%28k%2F2%29%5E2%29
Simplify:
highlight_green%28%28pi%29k%5E2%2F2%29


Ratio of bases to total:
%28k%5E2%2F2%29%2F%28%28k%5E2%29%2F2%2Bk%5E2%29
'
%28k%5E2%29%2F%28k%5E2%2B2k%5E2%29
'
%28k%5E2%29%2F%28k%5E2%281%2B2%29%29
'
highlight%281%2F3%29