A large cube with edge length $3.6\text{ m}$ is to be completely filled with identical small cubes, each having a side length of $3\text{ cm}$. How many small cubes are needed?

Step-by-step solution

1. 1. Convert the large cube’s side from metres to centimetres: $3.6\text{ m}=360\text{ cm}$.
2. 2. Determine how many small cubes fit along one edge: $\frac{360}{3}=120$.
3. 3. Since the arrangement is a 3‑D grid, total cubes = $120^3$.
4. 4. Compute $120^3=120\times 120\times 120=1,728,000$.
5. 5. Thus 1,728,000 small cubes are required.
6. 6. The answer is 1,728,000.

Concept tested: Unit conversion and cubic packing

Published 16 October 2026 · How this solution was prepared and checked