The question asks: "Welche der beiden Schachteln kann mehr Inhalt fassen?" which translates to "Which of the two boxes can hold more content?"

Box 1 (Triangular Prism, Toblerone-shaped):

The dimensions are:

• Length: 17 cm
• Height: 2.6 cm
• Base width: 3 cm

The volume $V$ of a triangular prism is given by: $V = \frac{1}{2} \times \text{base width} \times \text{height} \times \text{length}$ Substituting the values: $V = \frac{1}{2} \times 3 \, \text{cm} \times 2.6 \, \text{cm} \times 17 \, \text{cm}$ $V = 1.5 \times 2.6 \times 17 = 66.3 \, \text{cm}^3$

Box 2 (Rectangular Prism):

The dimensions are:

• Length: 5 cm
• Width: 3 cm
• Height: 4 cm

The volume $V$ of a rectangular prism is given by: $V = \text{length} \times \text{width} \times \text{height}$ Substituting the values: $V = 5 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm}$ $V = 60 \, \text{cm}^3$

Conclusion:

The triangular prism (Toblerone-shaped box) has a volume of 66.3 cm³, while the rectangular box has a volume of 60 cm³. Therefore, the Toblerone-shaped box can hold more content.

Would you like further details or clarifications?

Here are five related questions for further exploration:

1. How does the surface area of each box compare?
2. What happens to the volume if the dimensions of the triangular box change?
3. Can you calculate the weight each box can hold if the density of the content is known?
4. How would you approach the problem if the box shapes were irregular?
5. What if one of the boxes had a lid with a thickness? How would that affect the volume?

Tip: Understanding different shapes' volume formulas is essential for solving packaging and storage problems efficiently.