A child makes a cuboid of plasticene of sides 6cm,3cm,and 4cm.How many such cuboids will be needed to form a cube?
Answers
Firstly , all the cubes used for making the cube will have the same volume as that of the cube.
So, let the required number of cuboids be n and side of new cube be x cm.
So, n ×( 6×3×4) = x3
Or, n× 72 = ×3
Clearly ,n is a number which when multiplied by 72 becomes a perfect cube.
Prime factorisation of 72= 2×2×2×3×3
Clearly ,3 must be multiplied to 72 to make it a perfect cube .
Therefore, n = 3.
Hence, we need 3 cuboids of those dimensions to make a cube. ANS
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Volume of the cube of sides 6 cm, 3 cm, 4 cm
= 6 cm × 3 cm × 4 cm = (3 × 3 × 2 × 2 × 2 ) cm3
Here, and one 3 are left which are not in a triplet.
If we multiply this expression by 3 , then it will become a perfect cube.
Thus, (3× 3 × 3 × 2 × 2 × 2) = 216 is a perfect cube. Hence, 3 cuboids are required to form a cube. ans