Shristi makes a cubical box of side 8cm,6cm,8cm.How many such cuboids will she need to make a perfect cube.
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Let n is the number of cuboids needed to make a perfect cube Dimensions of the cuboid are Length = 8 cm Breadth = 6 cm Height = 8 cm The side of a cube formed by the cuboids of dimensions (8cm x 6cm x 8cm) is in multiples of 8, 6 and 8 ⇒ LCM(8, 6 and 8) = 24 ∴ The smallest cube that has a side of length = 24 cm We have, Volume of cube = Side x Side x Side Volume so cuboid = Length x Breadth x Height As per the question ⇒ n x Volume of cuboid = Volume of cube ⇒ n x (8 x 6 x 8) = 24 x 24 x 24 ⇒ n = 36 ∴ Number of cuboids needed to make a perfect square = 36
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