Question : The radius of a metallic spherical ball is 3 cm. If the metallic ball is melted and recast into $x$ number of hemispheres of radius equal to half the radius of the metallic spherical ball, then find the value of $x$.
Option 1: 15
Option 2: 14
Option 3: 16
Option 4: 13
Correct Answer: 16
Solution :
Given,
Radius of sphere = 3 cm = $r_s$
Radius of hemisphere = $\frac{r_s}{2}$ = $r_h$
⇒ $r_s=2r_h$
We know, Volume of sphere = $x$(Volume of hemisphere) [in this case]
⇒ $\frac43\pi r_s^3=x(\frac23\pi r_h^3)$
⇒ $2(2r_h)^3=x(r_h)^3$
⇒ $x=2\times2\times2\times2$
⇒ $x=16$
Hence, the correct answer is 16.
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