A) \[1232\text{ }c{{m}^{3}}\]
B) \[1848\text{ }c{{m}^{3}}\]
C) \[1632\text{ }c{{m}^{3}}\]
D) \[1078\text{ }c{{m}^{3}}\]
Correct Answer: D
Solution :
\[2\pi rh:2\pi rh+2\pi {{r}^{2}}=1:2\] \[\Rightarrow \] \[2\pi rh:616=1:2\] \[\Rightarrow \] \[2\pi rh=\frac{616}{2}=308\] \[\therefore \] \[2\pi rh+2\pi {{r}^{2}}=616\] \[\Rightarrow \] \[308+2\pi {{r}^{2}}=616\] \[\Rightarrow \] \[2\pi {{r}^{2}}=308\] \[\Rightarrow \] \[{{r}^{2}}=\frac{308\times 7}{22\times 2}=49\] \[\Rightarrow \] \[r=7\] \[\therefore \] \[2\times \frac{22}{7}\times 7\times h=308\] \[\Rightarrow \] \[h=\frac{308}{44}=7\] \[\therefore \] Volume of cylinder \[=\pi {{r}^{2}}h\] \[=\frac{22}{7}\times 7\times 7\times 7=1078\,cu.cm.\]
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