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
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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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