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.
a) 3 : 7
b) 7 : 3
c) 6 : 7
d) 7 : 6
Answer: b
Explanation:
$$\eqalign{
& \frac{{\pi {r^2}h}}{{2\pi rh}} = \frac{{924}}{{264}} \cr
& \Rightarrow r = \left( {\frac{{924}}{{264}} \times 2} \right) \cr
& \Rightarrow r = 7\,m \cr} $$
$$\eqalign{
& \therefore 2\pi rh = 264 \cr
& h = \left( {264 \times \frac{7}{{22}} \times \frac{1}{2} \times \frac{1}{7}} \right) \cr
& h = 6\,m \cr} $$
Required ratio :
$$ = \frac{{2r}}{h} = \frac{{14}}{6} = 7:3$$
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