Railways
Sample Paper
RRB (Group D) Sample Test Paper-10
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, \[H=\frac{2}{3}\pi {{R}^{3}}\] .\[\therefore \,\,C\,\,:\,\,H=\frac{1}{3}\pi {{R}^{3}}:\,\,\frac{2}{3}\pi {{R}^{3}}=1:2\]