A cube has an edge length of 7 cm. If it is divided up into 1 cm cubes, how many 1 cm cubes are there?

Verified step by step guidance

insert step 1> Calculate the volume of the original cube using the formula for the volume of a cube: \( V = a^3 \), where \( a \) is the edge length of the cube.

insert step 2> Substitute the given edge length of the cube (7 cm) into the formula: \( V = 7^3 \).

insert step 3> Calculate the volume of the original cube.

insert step 4> Since each smaller cube has a volume of \( 1^3 = 1 \) cm\(^3\), the number of smaller cubes is equal to the volume of the original cube.

insert step 5> Determine the number of 1 cm cubes by dividing the volume of the original cube by the volume of one smaller cube.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Volume of a Cube

The volume of a cube is calculated using the formula V = a³, where 'a' is the length of one edge. For a cube with an edge length of 7 cm, the volume would be 7 cm × 7 cm × 7 cm, resulting in 343 cm³. This concept is essential for understanding how the total space within the cube can be quantified.

Unit Cubes

Unit cubes are the smallest cubes used to fill a larger volume, typically measuring 1 cm on each side. When determining how many unit cubes fit into a larger cube, the total volume of the larger cube is divided by the volume of a unit cube (1 cm³). This concept helps visualize and calculate the number of smaller cubes that can occupy the same space.

Division of Volume

To find out how many smaller cubes fit into a larger cube, the total volume of the larger cube is divided by the volume of the smaller cube. In this case, dividing the volume of the 7 cm cube (343 cm³) by the volume of a 1 cm cube (1 cm³) gives the total number of 1 cm cubes. This division is a fundamental operation in determining how many discrete units can fit into a given space.