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We are given a triangular prism with a height of 7 cm, a triangular base with a height of 4 cm, and a base width of 3 cm. The factory uses a total of **14.112 cm³** of cheese to make several pieces, each shaped like this prism.

We need to find how many pieces the factory made.

### Steps to solve:

1. **Volume of the triangular prism**: 
   The volume \( V \) of a triangular prism is calculated as:
   \[
   V = \text{Area of triangular base} \times \text{height of the prism}
   \]

   The area \( A \) of the triangular base is:
   \[
   A = \frac{1}{2} \times \text{base of the triangle} \times \text{height of the triangle}
   \]
   Here, the base of the triangle is 3 cm, and the height of the triangle is 4 cm.

   So, the area of the triangular base is:
   \[
   A = \frac{1}{2} \times 3 \, \text{cm} \times 4 \, \text{cm} = 6 \, \text{cm}^2
   \]

2. **Volume of one prism piece**:
   The volume of the triangular prism is:
   \[
   V = 6 \, \text{cm}^2 \times 7 \, \text{cm} = 42 \, \text{cm}^3
   \]

3. **Total number of pieces**:
   To find the number of pieces, we divide the total volume of cheese by the volume of one piece:
   \[
   \text{Number of pieces} = \frac{14.112 \, \text{cm}^3}{42 \, \text{cm}^3}
   \]

   Let me calculate this value for you.The calculation shows that the factory would make approximately **0.336** pieces, which is less than one full piece. This suggests the total volume of cheese provided (14.112 cm³) is not sufficient to make even a single full piece of the triangular prism, which requires 42 cm³.

Would you like more details on the calculations or further clarification? Here are five related questions to deepen understanding:

1. How would the number of pieces change if the dimensions of the prism were doubled?
2. What is the relationship between the shape's surface area and its volume?
3. How would the total number of pieces change if the total volume of cheese were increased to 50 cm³?
4. How do you calculate the surface area of a triangular prism?
5. How does changing the height of the prism affect the volume?

**Tip:** When calculating the volume of a shape, ensure all dimensions are in the same units to avoid conversion errors.

A factory makes cheese snacks. Each piece is in the shape of a triangular prism with dimensions: 3 cm base, 4 cm height of the triangle, and 7 cm height of the prism. The factory made pieces that required a total of 14.112 cm³ of cheese. How many pieces did the factory make?

Learn how to calculate the number of triangular prism-shaped cheese snacks a factory can make using a total of 14.112 cm³ of cheese. This problem covers key geometry concepts, including volume calculation of a triangular prism. Suitable for students in Grades 6-8.

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