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 cm

Let the volume of the cube to be formed from given cuboids = x cm

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

Volume of 1 cuboid = 5 x 5 x 2 = 50 cm

^{3}Let the volume of the cube to be formed from given cuboids = x cm

^{3}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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