The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924

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Question

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
$$\eqalign{
& \frac{{\pi \,{r^2}h}}{{2\pi \,rh}} = \frac{{924}}{{264}}\, \cr
& \Rightarrow r = {\frac{{924}}{{264}} \times 2} = 7m \cr
& {\text{And}},\,2\pi rh = 264 \cr
& \Rightarrow h = {264 \times \frac{7}{{22}} \times \frac{1}{2} \times \frac{1}{7}} = 6m \cr
& \therefore {\text{Required}}\,{\text{ratio}} \cr
& = \frac{{2r}}{h} = \frac{{14}}{6} = 7:3 \cr} $$

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