# Cost of a can (check my answer please)

Question goes...A can is in the shape of a circular cylinder is required to have a volume of 750 cubic centimeters. The top and bottom are made of material that costs 8 cents per square centimeter while the sides are made of a material that costs 5 cents per square centimeter. Express the total cost $C$ of the material as a function of the radius $r$ of the cylinder. For what value of $r$ is the cost $C$ the least?

Here's what I did but for some reason I'm not too confident with it.

Top and bottom: 2 circles; area of circle is $\pi r^2$, so total area is $2\pi r^2$.

Side: Lateral surface area is $2\pi rh$.

$C=2\pi r^2(.08)+2\pi rh(.05)$.

$V=\pi r^2h$

$750=\pi r^2h$

$h=\frac{750}{\pi r^2}$

So now $C=2\pi r^2(.08)+2\pi r\left(\frac{750}{\pi r^2}\right)$

$C=.16\pi r^2+.1\pi r\left(\frac{750}{\pi r^2}\right)$

$C=.16\pi r^2+\frac{75}{r}$ (multiply $16\pi r^2$ by $r$ to get same denominator)

$C=\frac{.16\pi r^3+75}{r}$.