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The problem asks for the total volume of cheese required to produce 390 pieces of cheese snacks, each shaped like a triangular prism.

### Step-by-Step Solution:

1. **Volume of a Triangular Prism:**
   The volume \( V \) of a triangular prism is given by:
   \[
   V = \text{Area of triangular base} \times \text{height of the prism}
   \]
   
   The area \( A \) of the triangular base is:
   \[
   A = \frac{1}{2} \times \text{base} \times \text{height of the triangle}
   \]
   From the image, the base of the triangle is 4 cm, and the height of the triangle is 3 cm. Therefore:
   \[
   A = \frac{1}{2} \times 4 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2
   \]
   
2. **Height of the Prism:**
   The height (or length) of the prism is 5 cm, as shown in the image.

3. **Volume of One Prism:**
   Now, the volume of one piece of cheese (one prism) is:
   \[
   V = 6 \, \text{cm}^2 \times 5 \, \text{cm} = 30 \, \text{cm}^3
   \]

4. **Total Volume for 390 Pieces:**
   The total volume required for 390 pieces is:
   \[
   \text{Total volume} = 30 \, \text{cm}^3 \times 390 = 11,700 \, \text{cm}^3
   \]

So, the total volume of cheese needed to make 390 pieces is **11,700 cubic centimeters**.

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Do you have any questions or would you like more details on any part?

Here are 5 related questions to expand on the topic:
1. How would the volume change if the height of the triangular base was doubled?
2. What is the formula for the surface area of a triangular prism?
3. How would you calculate the volume if the prism had a slanted height instead of a right angle?
4. What happens to the volume if both the height and the base of the triangular face are halved?
5. How could you find the mass of the cheese if its density is known?

**Tip:** Always check units when working with volume to ensure they match the required answer format (e.g., cubic centimeters).

A factory makes cheese snacks. Each piece is in the shape of a triangular prism. If the factory makes 390 such pieces, how much cheese will be needed to make all of them (in cubic centimeters)?

Learn how to calculate the total volume of 390 cheese snacks, each shaped like a triangular prism, with detailed steps using key geometry formulas. Suitable for middle school students (Grades 6-8).

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