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$$^2$$? [Use $$\pi = \frac{22}{7}$$]

Let's assume the radius of the large sphere and the small sphere is 'R' and 'r' respectively.

Let's assume the number of small spheres formed is 'N'.

the surface area of each small sphere is 2464 cm$$^2$$.

surface area of each small sphere = $$4\times\ \pi\ \times\ r^2\ =\ 2464$$

$$4\times\frac{22}{7}\ \times\ r^2\ =\ 2464$$

$$1\times\frac{1}{7}\ \times\ r^2\ =\ 28$$

$$r^2\ =\ 196$$

r = 14 cm

Volume of large sphere = N $$\times$$ volume of each small sphere

$$\frac{4}{3}\times\pi\times R^3\ =N\times\frac{4}{3}\times\pi\times r^3\ \ $$

$$\frac{4}{3}\times\pi\times28^3\ =N\times\frac{4}{3}\times\pi\times14^3\ \ $$

$$28^3\ =N\times14^3\ \ $$

the number of small spheres formed is 8.