SOLUTION: Cost of a Can. A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 6 cents per

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Question 891333: Cost of a Can. A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 6 cents per square centimeter, while the sides are made of material that costs 4 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder. What will the cost be if the radius is 10 centimeters?
Please help and/or give me an example on how to solve this particular problem. I thank you in advance.

Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
v = volume
r = radius
h =length of can or could be consdired as height
S = surface area
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v=pi%2Ar%5E2%2Ah
S=2%2Api%2Ar%5E2%2Bh%2A2pi%2Ar

You want S as a function of r, and you know v is a given constant, but h is unknown. You can use the v equation and solve for h and therefore eliminate h as a variable in the s equation.

h=v%2F%28pi%2Ar%5E2%29;
S=2pi%2Ar%5E2%2B%28v%2F%28pi%2Ar%5E2%29%292pi%2Ar
S=2pi%2Ar%5E2%2B%282pi%2Ar%2Av%29%2Fr%5E2
highlight%28S=2pi%2Ar%5E2%2B2pi%2Av%2Fr%29

The cost of the can is only slightly more complicated. Track from where each term came. The top and bottom EACH is pi%2Ar%5E2. The circular shaped side is 2pi%2Av%2Fr.

highlight%28C=6%282pi%2Ar%5E2%29%2B4%282pi%2Av%2Fr%29%29.
Simply substitute your needed values for r, and v, and compute the value for C as cents for the can.