Volume of compound 3D shapes worksheet for math practice.

To solve the problem of finding the volumes of the compound 3D shapes, we need to break each shape into simpler geometric components (like cubes and rectangular prisms) and then calculate their volumes individually. Finally, we sum up the volumes of these components.

Section A:

#### 1)
The shape consists of two rectangular prisms:
- First prism: Dimensions are \(4 \, \text{cm} \times 2 \, \text{cm} \times 6 \, \text{cm}\).
- Second prism: Dimensions are \(2 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).

Volume Calculation:
\[
V_1 = 4 \times 2 \times 6 = 48 \, \text{cm}^3
\]
\[
V_2 = 2 \times 2 \times 2 = 8 \, \text{cm}^3
\]
\[
\text{Total Volume} = V_1 + V_2 = 48 + 8 = 56 \, \text{cm}^3
\]

#### 2)
The shape is a larger rectangular prism with a smaller rectangular prism removed from it.
- Larger prism: Dimensions are \(6 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm}\).
- Smaller prism: Dimensions are \(4 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).

Volume Calculation:
\[
V_{\text{larger}} = 6 \times 4 \times 4 = 96 \, \text{cm}^3
\]
\[
V_{\text{smaller}} = 4 \times 2 \times 2 = 16 \, \text{cm}^3
\]
\[
\text{Total Volume} = V_{\text{larger}} - V_{\text{smaller}} = 96 - 16 = 80 \, \text{cm}^3
\]

#### 3)
The shape consists of two rectangular prisms:
- First prism: Dimensions are \(5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).
- Second prism: Dimensions are \(3 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm}\).

Volume Calculation:
\[
V_1 = 5 \times 3 \times 2 = 30 \, \text{cm}^3
\]
\[
V_2 = 3 \times 3 \times 3 = 27 \, \text{cm}^3
\]
\[
\text{Total Volume} = V_1 + V_2 = 30 + 27 = 57 \, \text{cm}^3
\]

#### 4)
The shape consists of two rectangular prisms:
- First prism: Dimensions are \(4 \, \text{cm} \times 3 \, \text{cm} \times 1 \, \text{cm}\).
- Second prism: Dimensions are \(2 \, \text{cm} \times 2 \, \text{cm} \times 3 \, \text{cm}\).

Volume Calculation:
\[
V_1 = 4 \times 3 \times 1 = 12 \, \text{cm}^3
\]
\[
V_2 = 2 \times 2 \times 3 = 12 \, \text{cm}^3
\]
\[
\text{Total Volume} = V_1 + V_2 = 12 + 12 = 24 \, \text{cm}^3
\]

#### 5)
The shape consists of three rectangular prisms:
- First prism: Dimensions are \(6 \, \text{cm} \times 1 \, \text{cm} \times 2 \, \text{cm}\).
- Second prism: Dimensions are \(3 \, \text{cm} \times 1 \, \text{cm} \times 2 \, \text{cm}\).
- Third prism: Dimensions are \(3 \, \text{cm} \times 1 \, \text{cm} \times 1 \, \text{cm}\).

Volume Calculation:
\[
V_1 = 6 \times 1 \times 2 = 12 \, \text{cm}^3
\]
\[
V_2 = 3 \times 1 \times 2 = 6 \, \text{cm}^3
\]
\[
V_3 = 3 \times 1 \times 1 = 3 \, \text{cm}^3
\]
\[
\text{Total Volume} = V_1 + V_2 + V_3 = 12 + 6 + 3 = 21 \, \text{cm}^3
\]

#### 6)
The shape is a larger cube with a smaller cube removed from it.
- Larger cube: Side length is \(8 \, \text{cm}\).
- Smaller cube: Side length is \(4 \, \text{cm}\).

Volume Calculation:
\[
V_{\text{larger}} = 8^3 = 512 \, \text{cm}^3
\]
\[
V_{\text{smaller}} = 4^3 = 64 \, \text{cm}^3
\]
\[
\text{Total Volume} = V_{\text{larger}} - V_{\text{smaller}} = 512 - 64 = 448 \, \text{cm}^3
\]

Final Answers:

\[
\boxed{56, 80, 57, 24, 21, 448}
\]