https://file.aiquickdraw.com/mathbot/file/1728703915932kw46witb.jpg

The problem in the image asks to find the volume of the given 3D shape. The dimensions of the figure are:

- Height: 3 yards (left side)
- Width: 6 yards (bottom part)
- Depth: 9 yards (right side depth) and 4 yards (upper part).

It seems to be a composite shape, possibly a step or a stair-like figure. To calculate the volume, we can split it into two rectangular prisms:

### Step 1: Break into Two Rectangular Prisms
1. **Bottom rectangular prism:**
   - Length: 6 yards
   - Width: 9 yards
   - Height: 2 yards

2. **Top rectangular prism (step-like part):**
   - Length: 6 yards
   - Width: 4 yards
   - Height: 2 yards (the height difference)

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

1. **Volume of bottom prism:**
   \[
   V = \text{Length} \times \text{Width} \times \text{Height} = 6 \times 9 \times 2 = 108 \, \text{yd}^3
   \]

2. **Volume of top prism:**
   \[
   V = \text{Length} \times \text{Width} \times \text{Height} = 6 \times 4 \times 2 = 48 \, \text{yd}^3
   \]

### Step 3: Total Volume
\[
V_{\text{total}} = 108 + 48 = 156 \, \text{yd}^3
\]

Thus, the volume of the figure is **156 cubic yards (yd³)**.

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Would you like further details or have any questions about this? 

Here are five related questions for practice:
1. How would the volume change if the height of the top step were doubled?
2. How do you calculate the surface area of each rectangular prism individually?
3. What is the volume of a single cube if each side is 2 yards?
4. Can the figure be divided in another way to simplify the calculations?
5. How would the volume change if the depth of the larger step was 10 yards instead of 9?

**Tip:** When calculating volumes of composite shapes, always break the figure into simpler parts (like cubes or prisms) for easier calculation.

Find the surface area and the volume of the figure shown. Dimensions: Height of 3 yards, Width of 6 yards, Depths of 9 yards and 4 yards (composite figure).

This problem involves calculating the surface area and volume of a composite figure composed of two rectangular prisms. The solution breaks the shape into two prisms and uses the formula for the volume of rectangular prisms (Volume = Length × Width × Height).

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