A cubical box has an edge of 1 metre. Small solid cubes each having an edge of 10 cm are to be placed inside the box so that it is completely filled without gaps. How many such small cubes can be put inside the box?

Introduction / Context:
This question checks the understanding of relationships between units as well as volumes of cubes. The task is to determine how many smaller cubes of a given edge length can exactly fill a larger cubical box. It tests familiarity with converting metres to centimetres and the idea that the number of small cubes is the cube of the ratio of edge lengths, provided the packing is perfect and there are no gaps.

Given Data / Assumptions:

• Edge of large cube (box) = 1 m.
• Edge of each small cube = 10 cm.
• 1 m = 100 cm.
• The box is completely filled with no gaps.

Concept / Approach:
First, express both edge lengths in the same unit. After that, the number of small cubes along one edge of the large cube equals the ratio of the large edge to the small edge. Since the solid is three dimensional, the total number of cubes is that ratio raised to the power 3. Equivalently, we can compute the volume of the large cube and divide by the volume of one small cube.

Step-by-Step Solution:
Step 1: Convert the large cube edge from metres to centimetres. Edge of large cube = 1 m = 100 cm. Edge of small cube = 10 cm. Step 2: Compute how many small cubes fit along one edge. Number along one edge = 100 / 10 = 10. Step 3: Use three dimensional count. Total small cubes = 10 * 10 * 10 = 10^3 = 1000. Thus, 1000 small cubes can be fitted into the box.

Verification / Alternative check:
Volume method: Volume of large cube = (1 m)^3 = 1 cubic metre. One cubic metre equals 100 cm * 100 cm * 100 cm = 1,000,000 cubic centimetres. Volume of each small cube = 10^3 = 1000 cubic centimetres. Number of cubes = 1,000,000 / 1000 = 1000. This matches the earlier result.

Why Other Options Are Wrong:
Option A (10) and Option B (100) ignore one or two of the three dimensions respectively. Option D (10000) corresponds to 10^4 and would be correct only if there were an extra dimension, which is not possible. Option E (500) is an arbitrary wrong value. Only 1000 is consistent with the geometry and unit conversion.

Common Pitfalls:
Some candidates forget to convert metres to centimetres and directly divide 1 by 10, giving 0.1 as a misleading ratio. Others compute surface area instead of volume or count along only one dimension. Always use consistent units and remember that a cube is three dimensional, so the number of small cubes is the cube of the linear ratio.

Final Answer:
A total of 1000 cubes of edge 10 cm can be placed inside the cubical box of edge 1 metre.