Question

The length, breadth and height of a cuboid is 14 cm, 26 cm and 38 cm respectively. If it is melted and cast into identical cubes of edge 2 cm, then find the number of identical cubes. 
1. 1629
2. 1739
3. 2729
4. 1729

Answer 1

Correct Answer - Option 4 : 1729

Given:

Length of a box = 14 cm

Breadth of a box = 26 cm

Height of a box = 38 cm

Side of the cube = 2 cm

Concept used:

Volume of cuboid = l × b × h

Volume of cube = (Side)3

Number of cubes formed from large cuboid = Volume of cuboid/Volume of cube

Calculation:

Volume of cuboid = 14 × 26 × 38

Volume of cube = 2³ = 8 

Number of cubes formed = (14 × 26 × 38)/8

⇒ 7 × 13 × 19

⇒ 1729

∴ The number of identical cubes is 1729.