A cube has edge 18 cm. How many smaller cubes of edge 3 cm can be cut from it?

To determine how many smaller cubes can be cut from a larger cube, we must compare their volumes.

• Foundational Concept: The volume of a cube is calculated by cubing its edge length (V = edge³). The number of smaller cubes that fit into a larger one is the ratio of their volumes.
• Correct Answer (216): The volume of the larger cube is 18 cm × 18 cm × 18 cm = 5832 cm³. The volume of a smaller cube is 3 cm × 3 cm × 3 cm = 27 cm³. Dividing the volume of the larger cube by the volume of the smaller cube (5832 / 27) yields 216. Alternatively, you can find how many smaller edges fit along one larger edge (18/3 = 6) and then cube that number (6³ = 216).
• Why other options are false: Options B (81), C (64), and D (144) are incorrect calculations that do not properly account for the three-dimensional nature of the problem.