Answer
$1.5$
Work Step by Step
We are given that $V=2 \ m^3$
Volume can be computed as: $V=\pi r^2 h$
or, $h=\dfrac{2}{\pi r^2}$
Next, the surface area is: $S=\pi r^2+2\pi rh$
Cost $= \pi r^2 (3)+2\pi r \times \dfrac{2}{\pi r^2}\times 2=3 \pi r^2 +\dfrac{8}{r}$
For minimum cost, we must have $\dfrac{dC}{dr}=0$
or, $6 \pi r -\dfrac{8}{r^2}=0$
or, $r=0.751 \ m$
Thus, $h=\dfrac{2}{3.14 (0.751)^2}=1.129 \ m$
Now, $\dfrac{h}{r}=\dfrac{1.129}{0.751}\approx 1.5$
