Find Rational Function C

mathdad

mathdad

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A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8¢ per square centimeter, while the sides are made of material that costs 5¢ per square centimeter. Find a rational function C that describes the total cost of the material as a function of the radius r of the cylinder.

I know:

The top and bottom areas are pi*r^2. So, the cost of the top and bottom must be 0.08*2*pi*r^2. Right?

The area of the side wall is 2pi*r*h. But I have to use the volume formula to get h in terms of r. Right?

The volume formula is pi*r^2*h.

Let V = 700.

700 = pi*r^2*h

Question:

Must I solve 700 = pi*r^2*h for h? If so, what is the next step? I must find C(r).
 
Yes, you will be solving the volume for h, then putting that into the cost function.

The cost function (in terms of both r and h) is 0.08*2*pi*r^2 + 0.05*2pi*r*h . Now replace h with your expression for it.
 
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