A warehouse has a cube-shaped storage space with each side measuring 4 m. This space is to be completely filled with identical small cubes, each having a side length of 2 cm. How many of these small cubes can fit inside the warehouse?

hard 5 marks Class 8 · Mathematics · Cubes and Cube Roots

Answer

8000000

The correct answer is 8000000 — Thus $8, 000, 000$ small cubes can be packed inside the warehouse.

Step-by-step solution

Convert the side of the large cube from metres to centimetres: $4, m = 400, cm$ .
Calculate the volume of the large cube: $(400, cm)^{3} = 64, 000, 000, cm^{3}$ .
Determine the volume of one small cube: $(2, cm)^{3} = 8, cm^{3}$ .
Divide the total volume by the volume of one cube: $64, 000, 000, cm^{3} /8, cm^{3} = 8, 000, 000$ .
Thus $8, 000, 000$ small cubes can be packed inside the warehouse.

Common mistake: Using metres instead of centimetres when computing volume, leading to a result 1,000 times too large.

Concept tested: Unit conversion and volume calculation