The curved surface area of a cylindrical pillar is 264 ${\mathrm{m}}^2$ and its volume is 924 ${\mathrm{m}}^3$. Find ratio of the diameter and the height of the pillar.

Let diameter and height of cylindrical pillar are 2r and h respectively. 

According to question

$\begin{array}{l}\frac{\pi r^{2}h}{2\pi rh}=\frac{924}{264}\\ \Rightarrow \frac{r}{2}=\frac{924}{264}\\ \Rightarrow r=\frac{924}{264}\times 2\\ =7\mathrm{m}\end{array}$

and $2\mathrm{\pi }\cdot \mathrm{h}=264$

$\begin{array}{l}\Rightarrow 2\times \frac{22}{7}\times 7\times h\\ =264\\ \Rightarrow h=\frac{264}{44}\\ =6\mathrm{m}\end{array}$

Hence, required ratio$=2\mathrm{r} :\mathrm{h}$

$$\begin{gathered} =2\times 7:6 \\ =7:3 \end{gathered}$$