Volume of Compound 3D shapes Worksheet | Fun and Engaging PDF ... - Free Printable

To solve the problem of finding the volume of the compound 3D shapes, we need to break each shape into simpler 3D shapes (like cubes and rectangular prisms) and then calculate the volume of each part separately. Finally, we sum up the volumes of all the parts to get the total volume of the compound shape.

Step-by-Step Solution:

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

Volume Calculation:
\[
\text{Volume of bottom prism} = 4 \times 2 \times 2 = 16 \, \text{cm}^3
\]
\[
\text{Volume of top prism} = 2 \times 2 \times 2 = 8 \, \text{cm}^3
\]
\[
\text{Total volume} = 16 + 8 = 24 \, \text{cm}^3
\]

#### 2)
The shape consists of two rectangular prisms:
- Left prism: Dimensions are \(5 \, \text{cm} \times 6 \, \text{cm} \times 2 \, \text{cm}\).
- Right prism: Dimensions are \(4 \, \text{cm} \times 6 \, \text{cm} \times 2 \, \text{cm}\).

Volume Calculation:
\[
\text{Volume of left prism} = 5 \times 6 \times 2 = 60 \, \text{cm}^3
\]
\[
\text{Volume of right prism} = 4 \times 6 \times 2 = 48 \, \text{cm}^3
\]
\[
\text{Total volume} = 60 + 48 = 108 \, \text{cm}^3
\]

#### 3)
The shape consists of three rectangular prisms:
- Bottom prism: Dimensions are \(5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).
- Middle prism: Dimensions are \(3 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm}\).
- Top prism: Dimensions are \(3 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm}\).

Volume Calculation:
\[
\text{Volume of bottom prism} = 5 \times 3 \times 2 = 30 \, \text{cm}^3
\]
\[
\text{Volume of middle prism} = 3 \times 3 \times 2 = 18 \, \text{cm}^3
\]
\[
\text{Volume of top prism} = 3 \times 2 \times 2 = 12 \, \text{cm}^3
\]
\[
\text{Total volume} = 30 + 18 + 12 = 60 \, \text{cm}^3
\]

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

Volume Calculation:
\[
\text{Volume of left prism} = 2 \times 3 \times 1 = 6 \, \text{cm}^3
\]
\[
\text{Volume of right prism} = 4 \times 2 \times 2 = 16 \, \text{cm}^3
\]
\[
\text{Total volume} = 6 + 16 = 22 \, \text{cm}^3
\]

#### 5)
The shape consists of three rectangular prisms:
- Left prism: Dimensions are \(5 \, \text{cm} \times 2 \, \text{cm} \times 5 \, \text{cm}\).
- Middle prism: Dimensions are \(3 \, \text{cm} \times 1 \, \text{cm} \times 7 \, \text{cm}\).
- Right prism: Dimensions are \(5 \, \text{cm} \times 1 \, \text{cm} \times 3 \, \text{cm}\).

Volume Calculation:
\[
\text{Volume of left prism} = 5 \times 2 \times 5 = 50 \, \text{cm}^3
\]
\[
\text{Volume of middle prism} = 3 \times 1 \times 7 = 21 \, \text{cm}^3
\]
\[
\text{Volume of right prism} = 5 \times 1 \times 3 = 15 \, \text{cm}^3
\]
\[
\text{Total volume} = 50 + 21 + 15 = 86 \, \text{cm}^3
\]

#### 6)
The shape is a large rectangular prism with a smaller rectangular prism removed from it.
- Large prism: Dimensions are \(8 \, \text{cm} \times 6 \, \text{cm} \times 4 \, \text{cm}\).
- Removed prism: Dimensions are \(4 \, \text{cm} \times 2 \, \text{cm} \times 4 \, \text{cm}\).

Volume Calculation:
\[
\text{Volume of large prism} = 8 \times 6 \times 4 = 192 \, \text{cm}^3
\]
\[
\text{Volume of removed prism} = 4 \times 2 \times 4 = 32 \, \text{cm}^3
\]
\[
\text{Total volume} = 192 - 32 = 160 \, \text{cm}^3
\]

Final Answers:

\[
\boxed{24, 108, 60, 22, 86, 160}
\]