Counting unit cubes in a larger cube: How many 10 cm × 10 cm × 10 cm cubes fit in a cube of edge 1 m?

Introduction / Context:
Partitioning a big cube into equal smaller cubes reduces to counting how many fit along each edge, then cubing that count (since the arrangement is 3D).

Given Data / Assumptions:

• Big cube edge = 1 m = 100 cm
• Small cube edge = 10 cm
• Number per edge = 100 / 10 = 10

Concept / Approach:
Total small cubes = (number per edge)^3 = 10^3 = 1000.

Step-by-Step Solution:
Along each edge: 10 cubesTotal: 10 * 10 * 10 = 1000

Verification / Alternative check:
Volume ratio method: (100^3) / (10^3) = 1,000,000 / 1000 = 1000, consistent.

Why Other Options Are Wrong:
10 and 100 count 1D/2D tilings, not 3D; 10000 is 10,000 which is 10^4, too large; 500 is arbitrary.

Common Pitfalls:
Forgetting the third dimension; mixing cm with m without converting; dividing volumes but forgetting cubes must tile exactly (they do here).

Final Answer:
1000