Integral calculus

Apr 2010

I am having problems with the following question.
I am getting lost in the wording.
Any help would be appreciated.

" A manufacturer of large enclosed cylindrical water tanks wants to know what dimensions he should make his tanks in order to minimize the amount of material used. In order to find the dimensions, first consider a 10,000 litre tank ( 10 cubic metres )"

a. Using the formula for the volume of a cylinder, express the height of the tank ( h metres) in terms of the radius ( r metres )

I have used the cylindrical volume formula and have the answer -:

h = 10,000/pi r^2

Is this correct ?

b. By using the expression in (a), express the surface area of the tank in terms of the radius only.

I have come up with -: ( s = surface area )

s = (20,000/r) + 2 pi r^2

Am I on the right path with these answers ?

Thank you