Question

A solid metal sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm. How many small spheres are made?

Solution

1. When a solid is melted and recast, the total volume stays the same.
2. Number of small spheres = volume of large sphere / volume of one small sphere.
3. Both volumes contain 4/3 x pi, so the ratio is r^3 / r^3 = 6^3 / 2^3 = 216 / 8.
4. 216 / 8 = 27, so 27 small spheres are made.