A certain number of identical spheres are formed by melting a large sphere of radius 28 cm. What is the number of small spheres formed if the surface area of each small sphere is 2464 cm ? [Use π = $\frac{22}{7}$]

8

We know that,

We know that the volume of the sphere = \(\frac{4}{3}\)πr³

According to the question,

4πr² = 2464

r² = 2464 × \(\frac{7}{88}\) 

r² = 196

r = 14

Volume of each smaller sphere = (\(\frac{4}{3}\)π14³) cm³

Let number of sphere can be made = x

According to the concept,

x(\(\frac{4}{3}\) × π × 14³) = (\(\frac{4}{3}\) × π × 28³)

= x × 14³ = 2³ × 14³

= x = 8