A soft drink can in the shape of a right circular cylinder is to have the capacity for 250mm^3. If the diameter of the can must be no less than 4cm and no greater than 8cm, find the dimensions of the can that will use the least amount of materials (include the top, bottom and side). What is the ratio of height:diameter of this can?

okay so I know the interval is $\displaystyle 4\le x \le8$ where x is the diameter

Is this the right equation to use in order to minimize?

$\displaystyle V = \pi (\frac{d}{2})^2h$ and d and h are the two variables so to eliminate one would this be correct? changing $\displaystyle \frac{d}{2} \Rightarrow r$ because it seems simpler to process $\displaystyle V=\pi r^2\frac{250}{\pi r^2}$