Can someone please explain this for me?

Calculus Optimization

1.Suppose we want to make a cylindrical can such that it holds 350 milliliters and we want the surface area to be as small as possible. What should we pick as the radius and the height? Round your answers to the nearest tenth of a centimeter. (You may want to look up the formulas for the surface area and volume of a cylinder. Keep as many decimal digits as you can until the very end of the problem.)

2.If we replace 350 milliliters with a constant k, what are the new values for the radius and height that we should pick? (You should not have to do the entire problem over from scratch. Try to see what happened to the 350 as you did your calculations for the first problem.)

3.Using your h and r from problem 2, find h/r and simplify - you should get a whole number. We can conclude that if you want to enclose a given volume with a cylinder, while minimizing the surface area, that you should pick your height and radius so that they have this ratio.

4.Now let's suppose that the material that is used for the top and bottom of the can costs more than the material that is used for the 'sides'. Specifically, the material for the top and bottom costs 0.2 cents per square centimeter and the material for the sides costs 0.1 cents per square centimeter. If you want your can to hold 350 milliliters and you want the cost to be as small as possible, what should we pick as the radius and height? Round your answers to the nearest tenth of a centimeter.

5.Compare your answers to number 1 and number 4. Using the fact that the material for the top and bottom is more expensive than the material for the sides, explain why it makes sense that your h-value in number 4 is higher than your h-value in number 1, and that your R-value in number 4 is lower than your R-value in number 1.

6.Now we'll be more general. Suppose the material for the top and bottom costs b cents per square centimeter and the material for the sides costs 0.1 cents per square centimeter. You want to make a can with a volume of k. What values for the height and radius will minimize the cost? (Your answer will have a k and a b in it.)

7.Find the ratio of h/r from the previous problem and simplify it. You should end up with an answer without a k in it. (It will still have a b in it.)