SOLUTION: Construct a rational function that will help solve the problem. Then, use a calculator to answer the question. A right circular cylinder is to have a volume of 45 cubic inches.

Algebra ->  Rational-functions -> SOLUTION: Construct a rational function that will help solve the problem. Then, use a calculator to answer the question. A right circular cylinder is to have a volume of 45 cubic inches.      Log On


   

Question 1128411: Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.
A right circular cylinder is to have a volume of 45 cubic inches. It costs 4¢/square inch to construct the top and bottom and 1¢/square inch to construct the rest of the cylinder. Find the radius to yield minimum cost. Let x = radius. (Round your answer to two decimal places.)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Thank you, but I'll use r for the radius instead of x; that's less confusing. I can call it x when I put the function in my calculator, since my calculator doesn't recognize the "r".

The cost is 4 cents per square inch for the top and bottom and 1 cent per square inch for the sides:

C%28r%29+=+4%282%28pi%29r%5E2%29%2B1%282%28pi%29rh%29

We need the function in terms of a single variable. To do that, we use the given volume and the formula for the volume to find the height h in terms of r:

45+=+%28pi%29r%5E2h
h+=+45%2F%28%28pi%29r%5E2%29

Now our cost function is in terms of r only:



Put that equation in your graphing calculator, graph it, and find the value of x (r) that gives the minimum function value (minimum cost).

Your graph should look something like this:
graph%28400%2C400%2C-1%2C5%2C-50%2C400%2C8%28pi%29x%5E2%2B90%2Fx%29