How many cubes of side 3 cm can be separated from a cube of side 15 cm?
2018
How many cubes of side 3 cm can be separated from a cube of side 15 cm?
Answer: C. 125 — ConceptFor cubes aligned edge to edge, divide the larger cube’s side length by the smaller cube’s side length to find how many smaller cubes fit along one…
- A.
25
- B.
27
- C.
125
- D.
144
Show answer & explanation
Correct answer: C
Concept
For cubes aligned edge to edge, divide the larger cube’s side length by the smaller cube’s side length to find how many smaller cubes fit along one dimension.
A cube has three perpendicular dimensions, so the total number is (larger side ÷ smaller side) cubed. This is also the ratio of their volumes.
Application
The number along each edge is 15 ÷ 3 = 5.
Therefore, the total number of smaller cubes is 5 × 5 × 5 = 125.
Cross-check
The volume ratio is 153 ÷ 33 = 3375 ÷ 27 = 125, which agrees with the edge-counting method.
Hence, 125 cubes of side 3 cm can be cut from the cube of side 15 cm.