Question : How many solid spheres of radius 3 cm can be formed by melting a bigger solid sphere of radius 24 cm?
Option 1: 512
Option 2: 128
Option 3: 64
Option 4: 256
Correct Answer: 512
Solution :
The radius of the bigger sphere, $R$ = 24 cm
The radius of the smaller spheres, $r$ = 3 cm
Let $N$ be the number of smaller spheres.
So, Volume of bigger sphere = number of smaller spheres × volume of smaller sphere
⇒ $\frac{4}{3} \pi R^3 = N × \frac{4}{3} \pi r^3$
⇒ $N = \frac{24^3}{3^3} = 8^3 = 512$
Hence, the correct answer is 512.
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