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

Solution :-
The volume of the cuboid = 10 cm × 7 cm × 2 cm
= 140 cm³
The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 10, 7 and 2.
The smallest such cube will have a side length of LCM of 10, 7 and 2.
LCM of 10, 7 and 2-
10 = 2×5
7 = 7
2 = 2
LCM = 2×5×7 = 70
The smallest such cube will have side length of 70 and volume (in cm³) of (70×70×70) cm³
Number of cuboids of volume (10×7×2) cm³ that will fit into a cube of volume (70×70×70) cm³
= (70×70×70) /(10×7×2)
= 343000/140
= 2450 cuboids
Answer.
So, Anu will need 2450 cubes to form a cube.

Answer 2

Hey there!

Given,

Dimensions of Cuboid = 10 * 7 * 2 .

Volume of cuboid = 140 CM³

=======================================

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

========================================

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

=========================================

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.