Question

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 1

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Given, side of the cube is 5 cm, 2 cm and 5 cm.

Therefore, volume of cube = 5×2×5 = 50

The prime factorisation of 50 = 2×5×5

Here, 2, 5 and 5 cannot be grouped into triples of equal factors.

Therefore, we will multiply 50 by 2×2×5 = 20 to get perfect square.

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Answer 2

Answer:

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm.

So, the dimension of the cube he needs to form will be the LCM of 5 and 2 = 10cm

Volume of cube he needs = a³

= 10³

= 1000cm³

And,

Volume of cuboid = l×b×h

= 5×2×5

= 50 cm³

So, Volume of cube = No of cuboids × volume of cuboid

$= > no \: of \: cuboids \: = \frac{vol \: of \: cube}{vol \: of \: cuboid}$

$= > no \: of \: cuboids = \frac{1000}{50} \\ = 20 \: cuboids$