question_answer

A cone is inscribed in a hemisphere such that their bases are common. If C is the volume of the cone and H that of the hemisphere, then what is the value of\[C:H\]?

A)  \[1:2\]           

B)         \[2:3\]             

C)         \[3:4\]             

D)         \[4:5\] 

Correct Answer: A

Solution :

Volume of cone, \[C=\frac{1}{3}\pi \,{{R}^{2}}H\]             \[=\frac{1}{3}\pi {{R}^{3}}\]                    \[(\because \,H=R)\] Volume of hemisphere, \[H=\frac{2}{3}\pi {{R}^{3}}\] \[\therefore \]     \[C:H=\frac{1}{3}\pi {{R}^{3}}:\frac{2}{3}\pi {{R}^{3}}=1:2\]