question_answer

A solid consists of circular cylinder with exact fitting right circular cone placed on the top. The height of the cone is h. If total  volume of the solid is three times the volume of  the cone, then the height of the circular cylinder is

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, \[\frac{\text{total}\,\text{volume}\,\text{of}\,\text{the}\,\text{solid}\,}{\text{Volume}\,\text{of}\,\text{circular}\,\text{cone}}\text{=}3\]             \[\Rightarrow \]   \[\frac{\pi {{r}^{2}}H+\frac{1}{3}\pi {{r}^{2}}h}{\frac{1}{3}\pi {{r}^{2}}h}=3\]             \[\Rightarrow \]   \[\pi {{r}^{2}}H+\frac{1}{3}\pi {{r}^{2}}h=\pi {{r}^{2}}h\] \[\Rightarrow \]   \[\pi {{r}^{2}}H=\frac{2}{3}\pi {{r}^{2}}h\] \[\Rightarrow \]   \[H=\frac{2}{3}h\]