Question

How many cuboids of sides 6 cm, 4 cm and 2 cm are needed to form a cube? Pls explain along with the answer

Answer 1

Answer:

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) = x3x3

Or, n× 96 = ×3×3

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.