$\begin{align}  & \text{Volume of an hemisphere is }=\tfrac{2}{3}\pi {{r}^{3}} \\ & \tfrac{2}{3}\pi {{r}^{3}}=718\tfrac{2}{3} \\ & \tfrac{2}{3}\times \tfrac{22}{7}\times {{r}^{3}}=\tfrac{2156}{3} \\ & {{r}^{3}}=\frac{2156}{3}\times \frac{7}{22}\times \frac{3}{2} \\ & {{r}^{3}}=49\times 7 \\ & r=\sqrt[3]{7\times 7\times 7}=7 \\\end{align}$