SOLUTION: The height of the cylinder is three times the diameter of the base. The surface area of the cylinder is 126. What is the radius of the base

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Question 751782: The height of the cylinder is three times the diameter of the base. The surface area of the cylinder is 126. What is the radius of the base
Found 2 solutions by josgarithmetic, tommyt3rd:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Say the diameter is d and the radius is d%2F2.
Let h= height of the cylinder.

h=3%2Ad

circumference is the LENGTH of the rounded side. This circumference is 2%2Api%2A%28d%2F2%29, or
circumference is d%2Api

The surface area then is h%2A%28d%2Api%29=3%2Ad%2A%28d%2Api%29=3d%5E2%2Api
and you were given in the description:
highlight%283d%5E2%2Api=126%29.
Solving for d is uncomplicated.

Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
h=3d=3(2r)=6r

%0D%0AA%5Bs%5D=2%2Api%2Ar%5E2%2Bh%282%2Api%2Ar%29%0D%0A



%0D%0AA%5Bs%5D=2%2Api%2Ar%5E2%2B6r%282%2Api%2Ar%29=14%2Api%2Ar%5E2%0D%0A

so that

%0D%0A126=14%2Api%2Ar%5E2%0D%0A
%0D%0Ar=3%2Fsqrt%28pi%29%29%0D%0A

:)