Debnath has made a cuboid whose length, breadth and height are 4 cm, 3 cm and 2 cm respectively. Let’s see how many cuboids of this type will form a cube.

Given that,

Debnath made a cuboid of dimension:

Length = 4 cm

Breadth = 3 cm

Height = 2 cm

Since, volume of cuboid = length × breadth × height

⇒ Volume of cuboid = 4 × 3 × 2

= 24

Therefore, volume of a cuboid made by Debnath is 24 cm³.

Factors of 24 are:

24 = 2 × 2 × 2 × 3

This 24 cm³ is volume of one cuboid, which is not even perfect cube.

And to form a cube, we need to have perfect cube volumes.

So make 24 into a perfect cube.

Notice the factors of 24,

24 = 2 × 2 × 2 × 3

Group three similar integers, we get

24 = (2 × 2 × 2) × 3

Multiply both sides by (3 × 3), we get

24 × (3 × 3) = (2 × 2 × 2) × 3 × (3 × 3)

⇒ 216 = (2 × 2 × 2) × (3 × 3 × 3)

Number of cuboids = (3 × 3)

Because multiplying (3 × 3) makes a cube by the same number of cuboids.

⇒ Number of cuboids = 9

Thus, number of required cuboids are 9.