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Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will be needed to form a cube?

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will be needed to form a cube?

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Solution: The sides of the cuboid are given as 5 cm, 2 cm and 5 cm. Volume of the cuboid = 5 cm × 2 cm × 5 cm = 50 cm3 For the prime factorisation of 50, we have 50 = 2 × 5 × 5 To make it a perfect cube, we must have 2 × 2 × 2 × 5 × 5 × 5 = 20 × (2 × 5 × 5) = 20 × volume of the given cuboid Thus, the required number of cuboids = 20.

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