Question

How many cuboids of dimensions 4cm x 3cm x 8cm will be needed to form a cube?

Answer 1

Step-by-step explanation:

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 ×( 8×3×4) =  x3  

Or, n× 96 =  ×3  

Clearly ,n is a number which when multiplied by 96 becomes a perfect cube.

Prime factorisation of 96= 2×2×2×2×2×3

Clearly , 2×3×3 ,i.e, 18 must be multiplied to 96 to make it a perfect cube .

Therefore, n = 18.

Hence, we need 18 cuboids of those dimensions to make a cube.

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Answer 2

Answer:

18

Step-by-step explanation:

Firstly , all the cuboids used for making the cube will have the same volume as that of the cube.

So,

n x 4x3x8 = x^3

where n = no. of cuboids needed to form cube

x = cube

therefore,

n x 96 = x^3

96 = 2×2×2×2×2×3

2×3×3 = 18 must be multiplied to 96 to form a perfect cube.

Therefore,

n = 18

Hence, we need 18 cuboids of those dimensions to make a cube.

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