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

To solve the problem of finding the volume of composite figures, we need to break each figure into simpler shapes (rectangular prisms) and calculate their volumes individually. Then, we sum up the volumes of these simpler shapes to get the total volume of the composite figure.

Problem 1:

The figure is an "L"-shaped prism. We can break it into two rectangular prisms:
- Prism 1: Dimensions are \(12 \, \text{ft} \times 9 \, \text{ft} \times 3 \, \text{ft}\).
- Prism 2: Dimensions are \(6 \, \text{ft} \times 3 \, \text{ft} \times 3 \, \text{ft}\).

#### Volume Calculation:
1. Volume of Prism 1:
\[
V_1 = \text{length} \times \text{width} \times \text{height} = 12 \times 9 \times 3 = 324 \, \text{ft}^3
\]

2. Volume of Prism 2:
\[
V_2 = \text{length} \times \text{width} \times \text{height} = 6 \times 3 \times 3 = 54 \, \text{ft}^3
\]

3. Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 324 + 54 = 378 \, \text{ft}^3
\]

Problem 2:

The figure is a combination of a rectangular prism on top of another rectangular prism.
- Top Prism: Dimensions are \(27 \, \text{in} \times 18 \, \text{in} \times 3 \, \text{in}\).
- Bottom Prism: Dimensions are \(27 \, \text{in} \times 18 \, \text{in} \times 5 \, \text{in}\).

#### Volume Calculation:
1. Volume of Top Prism:
\[
V_1 = \text{length} \times \text{width} \times \text{height} = 27 \times 18 \times 3 = 1458 \, \text{in}^3
\]

2. Volume of Bottom Prism:
\[
V_2 = \text{length} \times \text{width} \times \text{height} = 27 \times 18 \times 5 = 2430 \, \text{in}^3
\]

3. Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 1458 + 2430 = 3888 \, \text{in}^3
\]

Problem 3:

The figure is a combination of three rectangular prisms.
- Prism 1: Dimensions are \(11 \, \text{yd} \times 8 \, \text{yd} \times 3 \, \text{yd}\).
- Prism 2: Dimensions are \(8 \, \text{yd} \times 8 \, \text{yd} \times 3 \, \text{yd}\).
- Prism 3: Dimensions are \(8 \, \text{yd} \times 8 \, \text{yd} \times 3 \, \text{yd}\).

#### Volume Calculation:
1. Volume of Prism 1:
\[
V_1 = \text{length} \times \text{width} \times \text{height} = 11 \times 8 \times 3 = 264 \, \text{yd}^3
\]

2. Volume of Prism 2:
\[
V_2 = \text{length} \times \text{width} \times \text{height} = 8 \times 8 \times 3 = 192 \, \text{yd}^3
\]

3. Volume of Prism 3:
\[
V_3 = \text{length} \times \text{width} \times \text{height} = 8 \times 8 \times 3 = 192 \, \text{yd}^3
\]

4. Total Volume:
\[
V_{\text{total}} = V_1 + V_2 + V_3 = 264 + 192 + 192 = 648 \, \text{yd}^3
\]

Problem 4:

The figure is an "L"-shaped prism. We can break it into two rectangular prisms:
- Prism 1: Dimensions are \(11 \, \text{m} \times 8 \, \text{m} \times 3 \, \text{m}\).
- Prism 2: Dimensions are \(8 \, \text{m} \times 3 \, \text{m} \times 3 \, \text{m}\).

#### Volume Calculation:
1. Volume of Prism 1:
\[
V_1 = \text{length} \times \text{width} \times \text{height} = 11 \times 8 \times 3 = 264 \, \text{m}^3
\]

2. Volume of Prism 2:
\[
V_2 = \text{length} \times \text{width} \times \text{height} = 8 \times 3 \times 3 = 72 \, \text{m}^3
\]

3. Total Volume:
\[
V_{\text{total}} = V_1 + V_2 = 264 + 72 = 336 \, \text{m}^3
\]

Final Answers:

\[
\boxed{378 \, \text{ft}^3, 3888 \, \text{in}^3, 648 \, \text{yd}^3, 336 \, \text{m}^3}
\]