Q. 43.6( 190 Votes )

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

Answer :

Dimension of cuboid given = 5 x 5 x 2 cm
Volume of 1 cuboid = 5 x 5 x 2 = 50 cm3

Let the volume of the cube to be formed from given cuboids = x cm3
Now we know that this value x will be a perfect cube 
Number of cuboids x Volume of 1 cuboid = Volume of cube
Thus we can see that we have to multiply volume of 1 cuboid such that the resulting number is a perfect cube.
Thus, 50 x (Some number) = Perfect cube
Thus, 2 × 5 × 5 × n is a perfect cube
Now, to make this a perfect cube, minimum value of 'n' should be 2 × 2 × 5 (such that it has 3 factors of 2 and 5 each)
i.e. n = 20

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