Shruthi makes a cuboid of side 8 cm, 6 cm, 8 cm. How many such cuboids will she need to make a perfect cube?
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hii heres your answer
The volume of the cuboid (in cubic centimeters) = (8 x 6 x 8) cu cm
The cube is formed by stacking many such cuboids and it will have side
lengths which are multiple of 8, 6, and 8 cm.
The smallest such cube will have a side length of LCM(8, 6, 8) = 24 cm
and a volume (in cubic cm) of (24 x 24 x 24) cu cm.
Number of cuboids of volume (8 x 6 x 8) cu cm that will fit into a
cube of volume (24 x 24 x 24) cu cm.
= (24 x 24 x 24) / (8 x 6 x 8)
= 36.
Therefore, Shruthi needs 36 cuboids to make a perfect cube. hope it help you out
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The volume of the cuboid (in cubic centimeters) = (8 x 6 x 8) cu cm
The cube is formed by stacking many such cuboids and it will have side
lengths which are multiple of 8, 6, and 8 cm.
The smallest such cube will have a side length of LCM(8, 6, 8) = 24 cm
and a volume (in cubic cm) of (24 x 24 x 24) cu cm.
Number of cuboids of volume (8 x 6 x 8) cu cm that will fit into a
cube of volume (24 x 24 x 24) cu cm.
= (24 x 24 x 24) / (8 x 6 x 8)
= 36.
Therefore, Shruthi needs 36 cuboids to make a perfect cube. hope it help you out
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2
Answer:
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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