From the body of a solid cube of edge 7 cm, a solid sphere is removed…

From the body of a solid cube of edge 7 cm, a solid sphere is removed. The volume of the remaining solid was found to be $163 \frac{1}{3}$ cm³. What is the diameter (in cm) of the sphere?

$\left(\right.$Take $\pi=\frac{22}{7}$)