Answer
$r =0.682 \ m \approx 0.7 \ m$
Work Step by Step
We are given that $V=1 \ m^3$
Volume can be computed as: $V=\pi r^2 h$
or, $h=\dfrac{1}{\pi r^2}$
Next, the surface area is: $S= \pi r^2+2\pi rh= \pi r^2+2\pi r \times \dfrac{1}{\pi r^2}$
For minimum surface area, we must have $\dfrac{dS}{dr}=0$
or, $2 \pi r -\dfrac{2}{r^2}=0$
or, $r=\sqrt[3] {\dfrac{1}{\pi}}=0.682 \ m \approx 0.7 \ m$
