The radius and height of a cylinder are in the ratio 7 : 2.

We have: $\frac{\text { radius }}{\text { height }}=\frac{7}{2}$

i.e., $r=\frac{7}{2} h$

Now, volume $=\pi \mathrm{r}^{2} \mathrm{~h}=\pi\left(\frac{7}{2} \mathrm{~h}\right)^{2} \mathrm{~h}=8316 \mathrm{~cm}^{3}$

$\Rightarrow \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times h^{3}=8316$

$\Rightarrow h^{3}=\frac{8316 \times 2}{11 \times 7}=108 \times 2=216$

$\Rightarrow h=\sqrt[3]{216}=6 \mathrm{~cm}$

Then $r=\frac{7}{2} h=\frac{7}{2} \times 6=21 \mathrm{~cm}$

$\therefore$ Total surface area $=2 \pi \mathrm{r}(h+r)=2 \times \frac{22}{7} \times 21 \times(6+21)=3564 \mathrm{~cm}^{2}$