Question : How many spherical balls of radius 6 cm can be made by melting a hemisphere of radius 24 cm?
Option 1: 64
Option 2: 96
Option 3: 32
Option 4: 24
Correct Answer: 32
Solution :
Given: A spherical ball of radius 6 cm and a hemisphere of radius 24 cm.
The volume of the sphere = $\frac{4}{3}\pi r^3$
The volume of the hemisphere = $\frac{2}{3}\pi r^3$, where $r$ is the radius.
Let $x$ be the spherical balls made.
According to the question,
$x \times \frac{4}{3} \pi\times 6^3=\frac{2}{3}\pi \times{24}^3$
⇒ $x=2\times4\times4=32$
Hence, the correct answer is 32.
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