Imagine melting a large ball of clay into 27 equal-sized tiny marbles; the total amount of clay stays exactly the same, just divided into smaller pieces.

Volume stays the same when you melt and play a game!

The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$. Since the volume is conserved during the melting and recasting process, the relation is given by $V_{\text{large}} = 27 imes V_{\text{small}}$, which simplifies to $R^3 = 27 imes r^3$.

Always equate volumes when dealing with melting and recasting problems in mensuration.