https://file.aiquickdraw.com/mathbot/file/1731503815065b635qja1.jpg

To find the volume of this triangular prism, we'll use the formula:

\[
V = B \cdot h
\]

where:
- \( B \) is the area of the triangular base.
- \( h \) is the height (or length) of the prism, which is 32 cm in this case.

### Step 1: Calculate the Area of the Triangular Base
The base is a right triangle with dimensions:
- Height of the triangle = 6 cm
- Base of the triangle = 9 cm

The area \( B \) of a triangle is given by:

\[
B = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substitute the values:

\[
B = \frac{1}{2} \times 9 \times 6 = \frac{1}{2} \times 54 = 27 \text{ cm}^2
\]

### Step 2: Calculate the Volume of the Prism

Now, use the volume formula \( V = B \cdot h \):

\[
V = 27 \times 32 = 864 \text{ cm}^3
\]

### Answer
The volume of the triangular prism is:

\[
\boxed{864 \text{ cm}^3}
\]

Let me know if you'd like more details or have questions. Here are five related questions for further practice:

1. How would the volume change if the length of the prism were doubled?
2. What would be the volume if the triangular base dimensions were halved?
3. How can you calculate the surface area of this triangular prism?
4. If the height of the triangular base was 8 cm instead of 6 cm, what would be the new volume?
5. How would you calculate the volume if the base was not a right triangle?

**Tip:** For any prism, the volume is always the area of the base multiplied by the height (or length) of the prism.

The dimensions of a triangular prism are shown in the diagram. What is the volume of the triangular prism in cubic centimeters?

Learn how to calculate the volume of a triangular prism with a triangular base of 9 cm by 6 cm and a prism height of 32 cm. This problem covers essential geometry concepts, including the volume formula for prisms and the area calculation for triangles. Suitable for Grades 7-9 students.

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