How many cubes of side 3 cm can be separated from a cube of side 15 cm?

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

1. The number along each edge is 15 ÷ 3 = 5.

2. 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.