A 3 cm-radius solid metal sphere is melted and reshaped into smaller spheres, each with a 1 cm radius. From the original sphere, how many smaller spheres can be created?

Solution

The total volume remains unchanged when the metal is melted and reshaped. Since the volume of a sphere is \(V=\frac43\pi r^3\), the number of smaller spheres is \(\frac{\frac43\pi(3)^3}{\frac43\pi(1)^3}=\frac{27}{1}=27\). Trick: Number of smaller spheres \(=(\frac{\text{original radius}}{\text{smaller radius}})^3=(3/1)^3=27\).