Answer
707 pm
Work Step by Step
For a face-centered cubic arrangement there are $8 \times 1/8$ atoms in the corners and $6\times1/2$ in the faces, so 4 ions per unit cell. Since the potassium ions are in octahedral holes, there are also 4 potassium ions per unit cell.
Mass: $4\times (39.0983+126.905)\ g/mol\div 6.022\times 10^{23}\ ions/mol=1.103\times10^{-21}\ g/cell$
Volume: $1.103\times10^{-21}\ g/cell\div 3.12\ g/cm^3=3.534\times10^{-22}\ cm^3/cell$
Side-length: $\sqrt[3]{3.534\times10^{-22}\ cm^3}=7.07\times10^{-8}\ cm=707\ pm$
