Math worksheet for calculating the volume of compound solids with labeled dimensions.

To solve the problem of finding the volume of each compound solid, we need to break down each shape into simpler geometric solids (like cubes and rectangular prisms) and then calculate their volumes individually. Finally, we sum up the volumes of these simpler shapes to get the total volume of the compound solid.

Step-by-Step Solution:

#### 1. First Compound Solid:
- The shape consists of a cube and a rectangular prism.
- Cube: Side length = 4 cm
\[
\text{Volume of cube} = 4 \times 4 \times 4 = 64 \, \text{cm}^3
\]
- Rectangular Prism: Dimensions = 5 cm × 2 cm × 4 cm
\[
\text{Volume of rectangular prism} = 5 \times 2 \times 4 = 40 \, \text{cm}^3
\]
- Total Volume:
\[
\text{Total Volume} = 64 + 40 = 104 \, \text{cm}^3
\]

#### 2. Second Compound Solid:
- The shape consists of two rectangular prisms.
- First Rectangular Prism: Dimensions = 4 cm × 5 cm × 8 cm
\[
\text{Volume of first rectangular prism} = 4 \times 5 \times 8 = 160 \, \text{cm}^3
\]
- Second Rectangular Prism: Dimensions = 4 cm × 5 cm × 2 cm
\[
\text{Volume of second rectangular prism} = 4 \times 5 \times 2 = 40 \, \text{cm}^3
\]
- Total Volume:
\[
\text{Total Volume} = 160 + 40 = 200 \, \text{cm}^3
\]

#### 3. Third Compound Solid:
- The shape consists of two rectangular prisms.
- First Rectangular Prism: Dimensions = 8 cm × 7 cm × 4 cm
\[
\text{Volume of first rectangular prism} = 8 \times 7 \times 4 = 224 \, \text{cm}^3
\]
- Second Rectangular Prism: Dimensions = 9 cm × 5 cm × 4 cm
\[
\text{Volume of second rectangular prism} = 9 \times 5 \times 4 = 180 \, \text{cm}^3
\]
- Total Volume:
\[
\text{Total Volume} = 224 + 180 = 404 \, \text{cm}^3
\]

#### 4. Fourth Compound Solid:
- The shape consists of two rectangular prisms.
- First Rectangular Prism: Dimensions = 7 cm × 5 cm × 3 cm
\[
\text{Volume of first rectangular prism} = 7 \times 5 \times 3 = 105 \, \text{cm}^3
\]
- Second Rectangular Prism: Dimensions = 7 cm × 4 cm × 6 cm
\[
\text{Volume of second rectangular prism} = 7 \times 4 \times 6 = 168 \, \text{cm}^3
\]
- Total Volume:
\[
\text{Total Volume} = 105 + 168 = 273 \, \text{cm}^3
\]

#### 5. Fifth Compound Solid:
- The shape consists of two rectangular prisms.
- First Rectangular Prism: Dimensions = 4 cm × 5 cm × 6 cm
\[
\text{Volume of first rectangular prism} = 4 \times 5 \times 6 = 120 \, \text{cm}^3
\]
- Second Rectangular Prism: Dimensions = 2 cm × 5 cm × 6 cm
\[
\text{Volume of second rectangular prism} = 2 \times 5 \times 6 = 60 \, \text{cm}^3
\]
- Total Volume:
\[
\text{Total Volume} = 120 + 60 = 180 \, \text{cm}^3
\]

#### 6. Sixth Compound Solid:
- The shape consists of two rectangular prisms.
- First Rectangular Prism: Dimensions = 6 cm × 5 cm × 6 cm
\[
\text{Volume of first rectangular prism} = 6 \times 5 \times 6 = 180 \, \text{cm}^3
\]
- Second Rectangular Prism: Dimensions = 3 cm × 5 cm × 6 cm
\[
\text{Volume of second rectangular prism} = 3 \times 5 \times 6 = 90 \, \text{cm}^3
\]
- Total Volume:
\[
\text{Total Volume} = 180 + 90 = 270 \, \text{cm}^3
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 104 \, \text{cm}^3 \\
2. & 200 \, \text{cm}^3 \\
3. & 404 \, \text{cm}^3 \\
4. & 273 \, \text{cm}^3 \\
5. & 180 \, \text{cm}^3 \\
6. & 270 \, \text{cm}^3 \\
\end{array}
}
\]