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 :

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