The radius and height of a cylinder are in the ratio 7:2. If the volume of the cylinder is 8.316cm³, find the total surface area of the cylinder.

The radius and height of a cylinder are in the ratio 7:2.
So, suppose the radius and height of cylinder are 7x and 2x respectively.
Then, volume of cylinder = ${\mathrm{\pi r}}^2\mathrm{h} = \frac{22}{7}\times {\left(7\mathrm{x}\right)}^2\times 2\mathrm{x} = \frac{22}{7}\times 49{\mathrm{x}}^2\times 2\mathrm{x} = 308{\mathrm{x}}^3$
And the given volume of cylinder = $8.316 {\mathrm{cm}}^3$
So we have;
$$\begin{gathered} 308x^3 = 8.316 \\ \Rightarrow x^3 = \frac{8.316}{308} = 0.027 \\ \Rightarrow x^3 = {\left(0.3\right)}^3 \\ \Rightarrow x = 0.3 \end{gathered}$$
So, the radius of cylinder = $7\times 0.3$ = 2.1 cm
And the height of cylinder = $2\times 0.3$ = 0.6 cm
Total surface area of cylinder = $2\mathrm{\pi r}\left(\mathrm{r}+\mathrm{h}\right) = 2\times \frac{22}{7}\times 2.1\left(2.1+0.6\right)$
$$\begin{gathered} = 2\times \frac{22}{7}\times 2.1\times 2.7 \\ = 35.64 {\mathrm{cm}}^2 \end{gathered}$$