Question : A metallic solid sphere has a radius of 28 cm. If it is melted to form small spheres of radius 3.5 cm, then how many small spheres will be obtained?
Option 1: 512
Option 2: 624
Option 3: 496
Option 4: 424
Correct Answer: 512
Solution :
The radius of a large sphere, $R$ = 28 cm
The radius of a small sphere, $r$ = 3.5 cm
Let $n$ be the number of small spheres.
The volume of the large sphere = number of small spheres × volume of the small sphere
So, $\frac{4}{3} \pi R^3 = n × \frac{4}{3} \pi r^3$
$⇒ n = \frac{R^3}{r^3} = \frac{28^3}{3.5^3}= 512$
Hence, the correct answer is 512.
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