A cuboid of length 12 cm, breadth 8 cm and height 6 cm is cut into small cubes of side 2 cm each. How many such small cubes can be obtained?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 72
Each small cube has volume \(2^3=8\) cm3, and since 2 divides every edge exactly, the cubes fill the cuboid with nothing left over: number \(=\) volume of the cuboid \(\div\) volume of one cube.
Volume of the cuboid \(=12\times8\times6=576\) cm3
Volume of one cube \(=2\times2\times2=8\) cm3
Number of cubes \(=576\div8=72\) (that is \(6\times4\times3\) along the three edges)
Why the other options are incorrect
Option (2) 36 — Incorrect. This divides by 16; a 2 cm cube has volume 8 cm3, not 16 cm3.
Option (3) 576 — Incorrect. This is the volume of the cuboid, not the number of cubes.
Option (4) 48 — Incorrect. This is \(6\times4\times2\); the height 6 cm holds 3 cubes, not 2.