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Question

Amar made a cuboid of thermocol of dimensions 12 cm, 10 cm and 6 cm. How many minimum number of such cuboids will be needed to form a cube?

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Solution

The volume of the cuboid = 12 cm × 10 cm × 6 cm

= 720 cu cm

The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 12, 10 and 6.

The smallest such cube will have a side length of LCM of 12, 10 and 6.

LCM of 12, 10 and 6 -

12=2×2×310=2×56=3×2LCM=2×2×3×5=60

The smallest such cube will have side length of 60 and volume (in cu. cm) of (60×60×60) cu. cm.

Number of cuboids of volume (12×10×6) cu. cm that will fit into a cube of volume (60×60×60) cu cm.

= 60×60×6012×10×6
= 300 cuboids

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