A cylindrical container must be constructed to contain 250 cubic inches of liquid.

A cylindrical container must be constructed to contain 250 cubic inches of liquid.

A. Express the entire surface area of the container as a function of its radius r and height h. Don’t forget the top and bottom.

B. Express the volume as a function of r and h, and set this expression equal to 250.

C. Use your work from part b to solve for h in terms of r. Then substitute this expression for h into your area expression from part a.

D. Using a graphing technique, find the value of r that makes the surface area a minimum.

E. What dimensions of the container should the manufacturer use if his goal is to minimize the amount of material used in its manufacture?

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