optimization problem calculus

You got lucky Mr. Hui. If you showed that for your work on a test, you probably would've gotten marked off. Your first mistake was that you didn't read the formula. The problem says you are trying to minimize the COST. In your work you minimized the SURFACE AREA. You would think they are the same thing, but you overlooked one fact, that the bottom area is worth TWICE as much as the sides of the swimming pool. To do it correctly you think of it as a cylinder with no top (because pools are open to the air, another mistake you made)

so you have the sides of the cylinder (given by equation 2(pi)rh) and you have the bottom circle (pi r^2)

however, since the bottom is worth twice as the sides you must multiply it by 2.
so your cost function is....
Cost = 2 [pi r^2] + 2(pi)rh
which, coincidentally is exactly your formula. then you solve it out like how Mr. Hui did. You just got lucky this time Mr. Hui. If the bottom were worth three times or any other number other than two, you would've gotten it wrong. Enjoy high school while you can....University level math isn't very forgiving for these kind of mistakes EVEN if you get the right answer...

[Mr. Hui]

Thanks for the clarification Cauchy. Luck was on my side.