Answer
$r=261.6m$
Work Step by Step
In an artificial gravity, centripetal force $F_c$ acts as the gravitational force, normally experienced as weight on earth. In other words, $$W=F_c=\frac{mv^2}{r}$$
Here, we want the astronauts to weight $1/2$ of their earth-weight, so $W=1/2mg$
$$\frac{1}{2}mg=\frac{mv^2}{r}$$ $$\frac{g}{2}=\frac{v^2}{r}$$ $$r=\frac{2v^2}{g}$$
We have $v=35.8m/s$ and $g=9.8m/s^2$ $$r=261.6m$$
