A) \[2\,h\]
B) \[\frac{2\,h}{3}\]
C) \[4\,h\]
D) \[\frac{3\,h}{2}\]
Correct Answer: B
Solution :
[b] Let the height of circular cylinder \[=H\] According to the question, \[\frac{\text{total}\,\text{volume}\,\text{of}\,\text{the}\,\text{solid}\,}{\text{Volume}\,\text{of}\,\text{circular}\,\text{cone}}\text{=}3\] \[\Rightarrow \] \[\frac{\pi {{r}^{2}}H+\frac{1}{3}\pi {{r}^{2}}h}{\frac{1}{3}\pi {{r}^{2}}h}=3\] \[\Rightarrow \] \[\pi {{r}^{2}}H+\frac{1}{3}\pi {{r}^{2}}h=\pi {{r}^{2}}h\] \[\Rightarrow \] \[\pi {{r}^{2}}H=\frac{2}{3}\pi {{r}^{2}}h\] \[\Rightarrow \] \[H=\frac{2}{3}h\] |
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