How many solid spheres of radius 3 cm can be formed by melting a bigger solid sphere of radius 24 cm?

Let's assume the radius of the smaller and bigger spheres are 'r' and 'R' respectively.

Let's assume the number of smaller spheres can be formed by melting a bigger one is 'n'.

Volume of bigger sphere = 3 $$\times$$ Volume of smaller sphere

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

$$\frac{4}{3}\times\ \pi\ \times\ 24^3\ =\ n\times\frac{4}{3}\times\ \pi\ \times\ 3^3$$

$$\ \left(8\times\ 3\right)^3\ =\ n\ \times\ 3^3$$

$$\ \left(8\right)^3\ =\ n$$

So 512 solid spheres of radius 3 cm can be formed by melting a bigger solid sphere of radius 24 cm.