The dimensions of the shipping container in the image are 40 feet (length), 8 feet (width), and 8 feet (height). The problem asks how many $27 \, \text{ft}^3$ cubes can fit into this container.

Step-by-step process:

1. Volume of the shipping container:
   The volume $V$ of the shipping container can be calculated as: $V_{\text{container}} = \text{length} \times \text{width} \times \text{height}$ Substituting the values: $V_{\text{container}} = 40 \, \text{ft} \times 8 \, \text{ft} \times 8 \, \text{ft} = 2560 \, \text{ft}^3$

2. Volume of one cube:
   Each cube has a volume of $27 \, \text{ft}^3$.

3. Number of cubes:
   To find the number of $27 \, \text{ft}^3$ cubes that can fit in the container, divide the volume of the container by the volume of one cube: $\text{Number of cubes} = \frac{V_{\text{container}}}{V_{\text{cube}}} = \frac{2560 \, \text{ft}^3}{27 \, \text{ft}^3} \approx 94.81$ Since we can't have a fraction of a cube, the number of full cubes that fit in the container is 94.

Final Answer:

You can fit 94 cubes of $27 \, \text{ft}^3$ into the shipping container.

Let me know if you need further details or have any questions!

Here are 5 related questions to expand this topic:

1. How would the number of cubes change if the shipping container's height was 9 feet?
2. What if the cubes were $1 \, \text{ft}^3$ instead of $27 \, \text{ft}^3$?
3. How much empty space would be left in the container after fitting 94 cubes?
4. Could the container fit cubes of $30 \, \text{ft}^3$, and if so, how many?
5. How would the number of cubes change if the dimensions of the container were in meters?

Tip: Remember to consider both volume and arrangement when solving packing problems, as not all volumes can be efficiently packed without empty space.