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