How Many Cubes of Side 2 cm Can Be Packaged in a Cubical Box with an Inner Side of 4 cm?

In this article, we will walk through the process of determining how many small cubes of side 2 cm can be packaged within a larger cubical box with an inner side of 4 cm. This involves a simple yet insightful geometric calculation that can be useful in various fields such as packaging, construction, and logistics.

Understanding the Geometry

Before we proceed with the calculation, let's break down the problem into its fundamental geometric components.

Volume of the Cubical Box

The volume of the larger cubical box is given by:

Volume of the box side3 4 cm times; 4 cm times; 4 cm 64 cm3

Volume of the Smaller Cubes

The volume of each smaller cube is calculated as follows:

Volume of one cube side3 2 cm times; 2 cm times; 2 cm 8 cm3

Calculating the Number of Small Cubes

To find out how many small cubes can fit into the larger box, we need to divide the volume of the larger box by the volume of one small cube:

Number of cubes Volume of the box / Volume of one cube 64 cm3 / 8 cm3 8

Visualizing the Arrangement

We can also visualize the arrangement of the smaller cubes within the larger box:

The 4 cm side of the box can accommodate two 2 cm cubes along each dimension (length, width, height). Along one edge, you can fit 4 cm / 2 cm 2 cubes. Thus, the total number of cubes that can fit is 2 × 2 × 2 8.

Conclusion

Therefore, you can package 8 cubes of side 2 cm within a cubical box with an inner side of 4 cm. This calculation is not only a practical exercise but also an excellent example of how basic geometric principles can be applied to solve real-world problems.