https://file.aiquickdraw.com/mathbot/file/1724317650087lp4bxw31.jpg

by first identifying the base, find the volume of the prism

To find the volume of the prism in the image, we first need to identify the base of the prism, then calculate the area of that base, and finally multiply by the height (or length) of the prism.

### Step 1: Identify the Base of the Prism
The base of the prism appears to be the "C" shaped face, which lies in the plane parallel to the 16 cm edge.

### Step 2: Calculate the Area of the Base
The base is a composite shape consisting of rectangles and possibly squares. To calculate the area:

1. The outer rectangle of the base has dimensions:
   - Length: 9 cm
   - Width: 10 cm
   So, the area of the full rectangle = \( 9 \, \text{cm} \times 10 \, \text{cm} = 90 \, \text{cm}^2 \).

2. The area of the cut-out portions:
   - The top cut-out has dimensions 5 cm by 3 cm, so its area = \( 5 \, \text{cm} \times 3 \, \text{cm} = 15 \, \text{cm}^2 \).
   - The bottom cut-out has dimensions 6 cm by 3 cm, so its area = \( 6 \, \text{cm} \times 3 \, \text{cm} = 18 \, \text{cm}^2 \).

   Total area of the cut-outs = \( 15 \, \text{cm}^2 + 18 \, \text{cm}^2 = 33 \, \text{cm}^2 \).

3. The effective area of the base:
   - Effective base area = \( 90 \, \text{cm}^2 - 33 \, \text{cm}^2 = 57 \, \text{cm}^2 \).

### Step 3: Calculate the Volume
The height (length) of the prism, perpendicular to the base, is given as 16 cm.

\[
\text{Volume} = \text{Area of the base} \times \text{Height} = 57 \, \text{cm}^2 \times 16 \, \text{cm} = 912 \, \text{cm}^3
\]

### Final Answer:
The volume of the prism is **912 cubic centimeters**.

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the surface area of this prism?
2. What would the volume be if the height of the prism were doubled?
3. How would the volume change if one of the cut-outs was removed?
4. Can the method used to find this volume be applied to other shapes?
5. How would you find the volume if the base shape were more complex?

**Tip:** When dealing with composite shapes, break them down into simpler geometric shapes, find the area of each, and then add or subtract these areas as needed to find the total area.

Learn how to calculate the volume of a prism by first identifying the base and then using the formula: Volume = Area of base × Height. This problem covers key geometric concepts, including prism geometry and volume calculation. Suitable for students in Grades 7-9.

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