Question

anu made a cuboid with dimensions 10cm,7cm and 2cm.What is the least no. of such cuboid needed to form a cube?

Answer 1

Hey there!

Given,

Dimensions of Cuboid = 10 * 7 * 2 .

Volume of cuboid = 140 CM³

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We know that, If a is the edge of cube, then it's volume = a³ . Therefore, the volume of cube should be a perfect cube

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Given, Volume of cuboid = 140

Factorising it.

140 = 2²*5*7 .

To make it a perfect cube we multiply by 2 * 5² *7² .

So, Now Probable volume of cube with smallest number of cuboids = 2³*5³*7³ = 343000 cm³

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Number of such cuboids required = Volume of Cube / Volume of cuboid = 343000/140 = 2450 .

Therefore number of least such cubiods Anu would require to make a cube is 2450 .

Another method of solving

We could have approached the same by taking LCM of dimensions and taking it as the edge of cube.

Answer 2

Heya friend
Here's Ur answer

If the dimensions of the cuboid are 10,7,2 and we know that all edges of a cube are equal
Then we need to find such a number which is divisible by all 10,7,2 as all three of them will be present in each side in definite numbers
So we will find the lcm
10=2*5
7=1*7
2=1*2
So lcm=70
Now if the lcm is 70then 70 is the side and so the volume of this cube will be (70)^3
=343000
And the volume of one cuboid is 10*7*2=140
So when dividing volume of cube by volume of cuboid we find that the number of cuboid required are 2450

Hope it's correct and helps