A) 7 : 6
B) 6 : 7
C) 3 : 7
D) 7 : 3
Correct Answer: D
Solution :
If r be radius of base and h the height, then Curved surface of cylindrical pillar \[=2\pi rh\] and volume \[=\pi {{r}^{2}}h\] \[\therefore \] \[2\pi rh=264\,\,{{m}^{2}}\] ?(i) \[\pi {{r}^{2}}h=924\,\,{{m}^{3}}\] ?(ii) On dividing Eq. (ii) by Eq. (i), we get \[\frac{\pi {{r}^{2}}h}{2\pi rh}=\frac{924}{264}\,\,m\] \[\Rightarrow \] \[\frac{r}{2}=\frac{924}{264}\,\,m\] \[\Rightarrow \] \[r=\frac{924\times 2}{264}\,\,m=7\,\,m\] \[\therefore \]Diameters \[=2\times 7=14\,\,m\] From Eq. (i), \[h=\frac{264}{\pi \times d}=\frac{264}{22\times 14}=6\,\,m\] \[\therefore \]Required ratio \[=\frac{14}{6}\]i.e., 7 : 3
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