| If a hemisphere is melted and four spheres of equal volume are made, then the radius of each sphere will be equal to [SSC (CGL) Mains 2015] |
A) \[\frac{1}{4}th\] of the radius of the hemisphere
B) radius of the hemisphere
C) 1/2 of the radius of the hemisphere
D) \[\frac{1}{6}th\] of the radius of the hemisphere
Correct Answer: C
Solution :
| Let the radius of hemisphere = R |
| and radius of each sphere = r |
| \[\therefore \] \[\frac{2}{3}\pi {{R}^{3}}=4\times \frac{4}{3}\pi {{r}^{3}}\]\[\Rightarrow \]\[\frac{1}{8}{{R}^{3}}={{r}^{3}}\] |
| \[\Rightarrow \] \[\frac{{{r}^{3}}}{{{R}^{3}}}=\frac{1}{8}\]\[\Rightarrow \]\[\frac{r}{R}=\frac{1}{2}\] |
| \[\therefore \] \[r=\frac{R}{2}\] |
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