$\begin{align}  & V=\tfrac{1}{3}\pi {{r}^{2}}h \\ & 38\tfrac{1}{2}c{{m}^{3}}=\tfrac{1}{3}\times \tfrac{22}{7}\times {{r}^{2}}\times 3cm \\ & \frac{77}{2}c{{m}^{3}}=\frac{1}{3}\times \frac{22}{7}\times {{r}^{2}}\times 3cm \\ & \frac{77}{2}c{{m}^{3}}=\frac{22r}{7}cm \\ & {{r}^{2}}=\frac{7\times 77c{{m}^{2}}}{22\times 2} \\ & r=\sqrt{\frac{49}{4}}cm \\ & r=\frac{7}{2}cm \\\end{align}$