A solid cuboid of dimensions 20 \text{ cm} \times 15 \text{ cm} \times 10 \text{ cm} is melted and recast into small cubes of side 2.5 \text{ cm} each. If 10% of the material is lost during recasting, the number of whole (complete) cubes cast is:

Explanation

Volume of cuboid = 20 \times 15 \times 10 = 3000 \text{ cm}^3. Available volume after 10% loss = 3000 \times 0.9 = 2700 \text{ cm}^3. Volume of one cube = (2.5)^3 = 15.625 \text{ cm}^3. Number of cubes = \frac{2700}{15.625} = 172.8. The number of complete cubes is 172.

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