https://file.aiquickdraw.com/mathbot/file/17306585658067pwbh818.jpg

To find the volume of this stepped figure, let's break it down into three rectangular sections (steps) and find the volume of each part individually. Then, we’ll add up the volumes.

Given dimensions:

1. **Bottom Step**: \( 12 \, \text{ft} \) (length) \(\times 4 \, \text{ft} \) (width) \(\times 2 \, \text{ft} \) (height)
2. **Middle Step**: \( 8 \, \text{ft} \) (length) \(\times 4 \, \text{ft} \) (width) \(\times 2 \, \text{ft} \) (height)
3. **Top Step**: \( 4 \, \text{ft} \) (length) \(\times 4 \, \text{ft} \) (width) \(\times 2 \, \text{ft} \) (height)

### Step-by-Step Calculation:

1. **Volume of Bottom Step**:
   \[
   V_1 = 12 \times 4 \times 2 = 96 \, \text{ft}^3
   \]

2. **Volume of Middle Step**:
   \[
   V_2 = 8 \times 4 \times 2 = 64 \, \text{ft}^3
   \]

3. **Volume of Top Step**:
   \[
   V_3 = 4 \times 4 \times 2 = 32 \, \text{ft}^3
   \]

### Total Volume:
\[
V_{\text{total}} = V_1 + V_2 + V_3 = 96 + 64 + 32 = 192 \, \text{ft}^3
\]

### Answer:
The total volume of the figure is:
\[
\boxed{192 \, \text{ft}^3}
\]

Would you like further clarification or have any questions about this solution?

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Here are some related questions for further exploration:

1. How would the volume change if the height of each step were doubled?
2. If each step had a different width, how would you approach calculating the volume?
3. How could this problem be represented in a real-world scenario (e.g., building design)?
4. What would happen if the steps were rounded, and how would that affect volume calculation?
5. How would you calculate the volume if the steps formed a pyramid shape instead?

**Tip**: For composite shapes, break them down into simpler parts, calculate each volume individually, and then sum them.

Find the volume of the figure. Round to the nearest hundredth, if necessary. (Figure is not to scale)

Learn how to find the volume of a stepped rectangular prism by breaking it down into three sections. This step-by-step guide covers volume calculation, composite shapes, and the formula for a rectangular prism. Ideal for Grades 6-8.

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