A cube of side 15 cm is cut into small cubes of side 3 cm each. How many such small cubes can be obtained?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 125
The number of small cubes is the volume of the big cube divided by the volume of one small cube; since 3 divides 15, no material is left over.
Along each edge: \(15\div3=5\) small cubes
Number of small cubes \(=5\times5\times5=125\)
By volume: \(15^3\div3^3=3375\div27=125\)
Why the other options are incorrect
Option (1) 27 — Incorrect. This is the volume of one small cube, \(3^3=27\) cm3, not the number of cubes.
Option (2) 120 — Incorrect. The count must be a perfect cube here (5 along each edge), and 120 is not one.
Option (4) 100 — Incorrect. 100 is not a perfect cube either, so it cannot be a count of the form \(n\times n\times n\); here it must be \(5^3=125\).