How many 1-cm cubes does it take to construct a cube that is 4 cm on each edge?

Verified step by step guidance

1. Understand that a cube's volume is calculated by cubing the length of one of its edges.
2. Calculate the volume of the larger cube by raising the edge length (4 cm) to the power of 3: \( V = 4^3 \).
3. Calculate the volume of a 1-cm cube, which is simply \( 1^3 = 1 \) cubic centimeter.
4. Determine how many 1-cm cubes fit into the larger cube by dividing the volume of the larger cube by the volume of a 1-cm cube.
5. The result of this division will give you the total number of 1-cm cubes needed to construct the larger cube.

Key Concepts

Volume of a Cube

The volume of a cube is calculated using the formula V = s³, where 's' is the length of one edge. For a cube with edges measuring 4 cm, the volume would be 4³ = 64 cm³. This concept is essential for determining how much space the larger cube occupies.

Unit Volume

A 1-cm cube has a volume of 1 cm³, which serves as the basic unit of measurement for volume in this context. Understanding unit volume is crucial for calculating how many such cubes fit into a larger volume, as it allows for straightforward division of the total volume by the volume of a single unit.

Division of Volumes

To find out how many smaller cubes fit into a larger cube, one must divide the volume of the larger cube by the volume of the smaller cube. In this case, dividing the volume of the 4 cm cube (64 cm³) by the volume of the 1 cm cube (1 cm³) yields the total number of smaller cubes that can fit inside.