SOLUTION: I have the answer, I need to know how to get there: A steel drum in the shape of a right cylinder is required to have a volume of 100 cubic feet. a) Express the amount A of mater

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Question 187618: I have the answer, I need to know how to get there:
A steel drum in the shape of a right cylinder is required to have a volume of 100 cubic feet.
a) Express the amount A of material required to make the drum as a function of the radius r of the cylinder : A(r)=2 x pi x r^2 + 200/r
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Volume of a Cylinder: V=pi%2Ar%5E2%2Ah


Solve for "h" to get h=V%2F%28pi%2Ar%5E2%29


Note: in the volume of a cylinder formula, there are two independent variables "r" and "h" (ie they determine what V will turn out to be). Since we want the final function to be in terms of "r", this means that we need to eliminate "h".



Since we know that the volume is 100 cubic feet, this means that V=100. So plug that in to get h=100%2F%28pi%2Ar%5E2%29


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Surface Area of a Cylinder: SA=2%2Api%2Ar%5E2%2B2%2Api%2Ar%2Ah


SA=2%2Api%2Ar%5E2%2B2%2Api%2Ar%2A%28100%2F%28pi%2Ar%5E2%29%29 Plug in h=100%2F%28pi%2Ar%5E2%29. Notice how "h" is now gone (see above).


SA=2%2Api%2Ar%5E2%2B%28200%2Api%2Ar%29%2F%28pi%2Ar%5E2%29%29 Multiply


Cancel out the common terms.


SA=2%2Api%2Ar%5E2%2B200%2Fr Simplify


So the function of radius r is A%28r%29=2%2Api%2Ar%5E2%2B200%2Fr