Answer
$4$
Work Step by Step
We are given that $V=250 \ cm^3$
Volume can be computed as: $V=\pi r^2 h$
or, $h=\dfrac{250}{\pi r^2}$
Next, the surface area is: $S=2\pi r^2+2\pi rh$
Cost $=2 \pi r^2 (0.02)+2\pi r \times \dfrac{250}{\pi r^2}\times 0.01=0.04 \pi r^2 +\dfrac{5}{r}$
For minimum cost, we must have $\dfrac{dC}{dr}=0$
or, $0.08 \pi r -\dfrac{5}{r^2}=0$
or, $r=2.70 \ cm$
Thus, $h=\dfrac{250}{\pi (2.70)^2}=10.92 \ cm$
Now, $\dfrac{h}{r}=\dfrac{10.92}{2.7}=4$
