A solid cube, whose each edge is of length $48 ext{ cm}$, is melted. Identical solid cubes, each of volume $64 ext{ cm}^3$, are made out of this molten cube, without any wastage. How many such small cubes are obtained?

Question

A solid cube, whose each edge is of length $48 	ext{ cm}$, is melted. Identical solid cubes, each of volume $64 	ext{ cm}^3$, are made out of this molten cube, without any wastage. How many such small cubes are obtained?

Accepted Answer

**Solution:**

1. Calculate the volume of the larger cube:
   $$	ext{Volume} = 48^3 = 48 	imes 48 	imes 48 = 110592 	ext{ cm}^3$$

2. Given the volume of each smaller cube is:
   $$64 	ext{ cm}^3$$

3. Number of smaller cubes formed is:
   $$n = \frac{	ext{Volume of larger cube}}{	ext{Volume of smaller cube}} = \frac{110592}{64} = 1728$$

**Answer:** $1728$

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