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The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
Options:
A .  3 : 7
B .  7 : 3
C .  6 : 7
D .  7 : 6
Answer: Option B
$$\eqalign{
& \frac{{\pi {r^2}h}}{{2\pi rh}} = \frac{{924}}{{264}} \cr
& \Rightarrow r = \left( {\frac{{924}}{{264}} \times 2} \right) \cr
& \Rightarrow r = 7\,m \cr} $$
And,
$$\eqalign{
& \therefore 2\pi rh = 264 \cr
& \Rightarrow h = \left( {264 \times \frac{7}{{22}} \times \frac{1}{2} \times \frac{1}{7}} \right) \cr
& \Rightarrow h = 6\,m \cr} $$
∴ Required ratio :
$$ = \frac{{2r}}{h} = \frac{{14}}{6} = 7:3$$

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