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The problem involves calculating the volume of wood used to make a paperweight. The paperweight is a cuboid with part of it carved out in the shape of a triangular prism. From the image:

### Given dimensions:
- **Cuboid dimensions**:
  - Length = 7 cm
  - Width = 6 cm
  - Height = 5 cm

- **Triangular prism dimensions** (the part carved out):
  - Height of triangular face = 3 cm
  - Base of triangular face = 4 cm
  - Depth of the prism = 6 cm

### Approach to solving:

1. **Volume of the cuboid**:  
   The volume of a cuboid is given by:
   \[
   V_{\text{cuboid}} = \text{length} \times \text{width} \times \text{height}
   \]
   Substituting the given dimensions:
   \[
   V_{\text{cuboid}} = 7 \times 6 \times 5 = 210 \, \text{cm}^3
   \]

2. **Volume of the triangular prism**:
   The volume of a triangular prism is calculated as:
   \[
   V_{\text{prism}} = \frac{1}{2} \times \text{base of triangle} \times \text{height of triangle} \times \text{depth}
   \]
   Substituting the values:
   \[
   V_{\text{prism}} = \frac{1}{2} \times 4 \times 3 \times 6 = 36 \, \text{cm}^3
   \]

3. **Volume of the wood used**:
   The volume of the wood is the volume of the cuboid minus the volume of the triangular prism:
   \[
   V_{\text{wood}} = V_{\text{cuboid}} - V_{\text{prism}} = 210 - 36 = 174 \, \text{cm}^3
   \]

Thus, the volume of the wood used to make the paperweight is **174 cubic centimeters**.

Do you want more details or have any questions?

Here are some related questions you might find interesting:
1. What is the formula for the surface area of a cuboid?
2. How do you calculate the surface area of a triangular prism?
3. What are some common applications of triangular prisms in real life?
4. How would the volume change if the dimensions of the cuboid doubled?
5. Can the triangular prism be replaced by a cylinder, and how would you calculate its volume?

**Tip:** Always break down complex shapes into simpler parts when solving volume problems.

Calculate the volume of wood used to make the paperweight. The paperweight is a cuboid with a triangular prism carved out.

Learn how to calculate the volume of wood used in a paperweight made of a cuboid with a carved triangular prism. The problem involves applying geometry formulas to find the volumes of both the cuboid and the triangular prism. Suitable for Grades 6-8.

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