https://r2.erweima.ai/mathbot/image/1725248108575lnvn55xj.jpg

To solve the problem shown in the image, let's analyze the dimensions of both the box and the cans:

### Box Dimensions:
- Length: 1.08 m
- Width: 0.54 m
- Height: 0.45 m

### Can Dimensions:
- Diameter: 8 cm (0.08 m)
- Height: 12 cm (0.12 m)

### Steps to Solve:
1. **Volume of the Box:**
   \[
   V_{\text{box}} = \text{Length} \times \text{Width} \times \text{Height} = 1.08 \, \text{m} \times 0.54 \, \text{m} \times 0.45 \, \text{m}
   \]
   \[
   V_{\text{box}} = 0.26244 \, \text{m}^3
   \]

2. **Volume of a Single Can:**
   The can is cylindrical, so its volume is calculated using:
   \[
   V_{\text{can}} = \pi \times \left(\frac{\text{Diameter}}{2}\right)^2 \times \text{Height} = \pi \times \left(\frac{0.08 \, \text{m}}{2}\right)^2 \times 0.12 \, \text{m}
   \]
   \[
   V_{\text{can}} = \pi \times 0.0016 \, \text{m}^2 \times 0.12 \, \text{m}
   \]
   \[
   V_{\text{can}} \approx 0.0006032 \, \text{m}^3
   \]

3. **Number of Cans That Can Fit in the Box:**
   The number of cans is determined by the total volume of the box divided by the volume of one can:
   \[
   \text{Number of cans} = \frac{V_{\text{box}}}{V_{\text{can}}} = \frac{0.26244 \, \text{m}^3}{0.0006032 \, \text{m}^3}
   \]
   \[
   \text{Number of cans} \approx 435.03
   \]

Given that only whole cans can be packed, we consider the number 435.

### Answer Selection:
Now, let's check the provided options:
- A) 378
- B) 425
- C) 250 x 2 = 500
- D) 278 x 2 = 556

The closest option to the calculated 435 is **option B) 425**.

Would you like any more details or have any other questions?

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Here are some related questions you might find interesting:

1. What happens if the dimensions of the box are slightly increased?
2. How would the solution change if the cans were stacked horizontally?
3. How would the problem change if the cans were of a different shape, such as rectangular prisms?
4. How would the situation change if some space needed to be left between the cans for safety?
5. What would be the impact on the number of cans if we considered the thickness of the box material?

**Tip:** When solving packing problems, always consider both the volume and the actual spatial arrangement. The optimal packing might require more than just simple volume calculations.

Learn how to calculate the volume of a box and a cylindrical can to determine the number of cans that can fit into the box. Detailed step-by-step solution with practical application of geometry and volume calculations. Suitable for high school students and math enthusiasts.

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