Packing small boxes in a large crate — convert meters to centimeters precisely: A wooden crate of inner dimensions 8 m × 7 m × 6 m is used to carry identical rectangular boxes of size 8 cm × 7 cm × 6 cm (no gaps). What is the maximum number of such boxes that can fit?

Introduction / Context:
This is a standard 3D packing by exact integer fit along each dimension. Convert the crateʼs dimensions to centimeters so they are commensurate with the small boxes, then multiply counts along each axis.

Given Data / Assumptions:

• Crate: 8 m × 7 m × 6 m = 800 cm × 700 cm × 600 cm
• Box: 8 cm × 7 cm × 6 cm
• Assume perfect orientation and no wasted space.

Concept / Approach:
Count per dimension = floor(L/ℓ) × floor(W/w) × floor(H/h).

Step-by-Step Solution:
Along 800/8 = 100Along 700/7 = 100Along 600/6 = 100Total = 100 * 100 * 100 = 1,000,000

Verification / Alternative check:
All divisions are exact integers; hence no leftover space in this idealized scenario.

Why Other Options Are Wrong:
They do not match the exact 100 × 100 × 100 fit.

Common Pitfalls:
Forgetting to convert meters to centimeters or mis-multiplying powers of 10.

Final Answer:
1000000