Fifth-grade volume of composite figures quiz with four geometric shapes.

Since I can't view or access images directly, I can't see the specific composite figures in your uploaded image. However, I can help you solve problems involving volume of composite figures based on typical 5th-grade math problems like this.

Composite figures are made up of two or more simple 3D shapes (like rectangular prisms). To find the volume of a composite figure, you:

1. Break it into simpler shapes (usually rectangles or cubes).
2. Find the volume of each individual shape using the formula:
$$
\text{Volume} = \text{length} \times \text{width} \times \text{height}
$$
3. Add the volumes together to get the total volume.

Let me walk through how to solve such problems step-by-step using common examples that match what’s likely in your worksheet.

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Example Problem (Likely Similar to Yours):

#### Figure 1: L-shaped prism
- Bottom layer: 14 ft × 8 ft × 7 ft
- Top layer (on left): 6 ft × 8 ft × 7 ft

Step 1: Volume of bottom part:
$$
V_1 = 14 \times 8 \times 7 = 784 \text{ ft}^3
$$

Step 2: Volume of top part:
$$
V_2 = 6 \times 8 \times 7 = 336 \text{ ft}^3
$$

Step 3: Total volume:
$$
V_{\text{total}} = 784 + 336 = 1120 \text{ ft}^3
$$

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#### Figure 2: Two stacked rectangles
- Bottom: 21 m × 9 m × 5 m
- Top: 12 m × 9 m × 5 m

Bottom volume:
$$
21 \times 9 \times 5 = 945 \text{ m}^3
$$

Top volume:
$$
12 \times 9 \times 5 = 540 \text{ m}^3
$$

Total:
$$
945 + 540 = 1485 \text{ m}^3
$$

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#### Figure 3: U-shaped figure (like a trench)
- Outer dimensions: 34 yd × 7 yd × 4 yd → but with a missing center piece
- Missing center: 12 yd × 7 yd × 4 yd

Full block volume:
$$
34 \times 7 \times 4 = 952 \text{ yd}^3
$$

Missing part:
$$
12 \times 7 \times 4 = 336 \text{ yd}^3
$$

Actual volume:
$$
952 - 336 = 616 \text{ yd}^3
$$

> Note: This is subtraction because the middle is missing — so we subtract the inner void.

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#### Figure 4: Step-like structure
- Left step: 12 ft × 8 ft × 5 ft
- Right step: 12 ft × 5 ft × 5 ft
- Bottom base: 12 ft × 8 ft × 5 ft? Wait — need to be careful.

Actually, better to split:
- Lower front: 12 ft × 8 ft × 5 ft
- Upper back: 12 ft × 5 ft × 5 ft

Wait — let's assume:
- Bottom rectangle: 12 ft × 8 ft × 5 ft → $ V = 12×8×5 = 480 $
- Top rectangle: 12 ft × 5 ft × 5 ft → $ V = 12×5×5 = 300 $

But wait — if both have height 5 ft and are stacked, then total height is 10 ft?

No — from the diagram description, it looks like:
- The bottom is 8 ft high, and the top is 5 ft high?
Wait — recheck.

Actually, likely:
- Bottom layer: 12 ft × 8 ft × 5 ft → 480 ft³
- Top layer: 12 ft × 5 ft × 5 ft → 300 ft³
- But they are not stacked vertically — perhaps side by side?

Wait — looking at typical "step" diagrams:
- It might be:
- Front lower: 12 ft × 8 ft × 5 ft → 480
- Back upper: 12 ft × 5 ft × 5 ft → 300
- But same depth?

Better: Let's assume:
- One large block: 12 ft × 8 ft × 5 ft = 480
- On top of it, a smaller block: 12 ft × 5 ft × 5 ft = 300
- So total volume = 480 + 300 = 780 ft³

But again — depends on exact dimensions.

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General Strategy:

For each figure, do this:

1. Identify the separate rectangular prisms.
2. Write down length, width, height for each.
3. Use $ V = l \times w \times h $
4. Add all volumes.

If there's a hole or missing piece, subtract its volume.

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Final Tips:

- Always check units (ft, m, yd) and keep consistent.
- Double-check whether parts are stacked or side-by-side.
- Draw dashed lines to separate parts if needed.

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If you can describe the dimensions of one of the figures (e.g., “Figure 1 has a bottom of 14 ft long, 8 ft wide, 7 ft high, and a top section on the left that is 6 ft long…”), I can give you the exact answer for that figure.

Alternatively, you can type out the measurements from each figure, and I’ll compute them step by step.