Volume of Compound Shapes Worksheets - Free Printable

To solve the problem of finding the volume of each rectangular prism, we need to break down each shape into simpler rectangular prisms and then calculate their volumes. The general formula for the volume of a rectangular prism is:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Let's go through each shape step by step.

---

Shape 1:

This shape can be divided into two rectangular prisms:
1. A larger rectangular prism with dimensions \(6 \times 2 \times 3\).
2. A smaller rectangular prism with dimensions \(4 \times 2 \times 2\).

#### Volume of the larger prism:
\[
\text{Volume}_{\text{large}} = 6 \times 2 \times 3 = 36
\]

#### Volume of the smaller prism:
\[
\text{Volume}_{\text{small}} = 4 \times 2 \times 2 = 16
\]

#### Total volume:
\[
\text{Total Volume} = 36 + 16 = 52
\]

Answer for Shape 1:
\[
\boxed{52}
\]

---

Shape 2:

This shape can be divided into two rectangular prisms:
1. A larger rectangular prism with dimensions \(5 \times 3 \times 3\).
2. A smaller rectangular prism with dimensions \(3 \times 3 \times 2\).

#### Volume of the larger prism:
\[
\text{Volume}_{\text{large}} = 5 \times 3 \times 3 = 45
\]

#### Volume of the smaller prism:
\[
\text{Volume}_{\text{small}} = 3 \times 3 \times 2 = 18
\]

#### Total volume:
\[
\text{Total Volume} = 45 + 18 = 63
\]

Answer for Shape 2:
\[
\boxed{63}
\]

---

Shape 3:

This shape can be divided into two rectangular prisms:
1. A larger rectangular prism with dimensions \(7 \times 2 \times 3\).
2. A smaller rectangular prism with dimensions \(5 \times 2 \times 2\).

#### Volume of the larger prism:
\[
\text{Volume}_{\text{large}} = 7 \times 2 \times 3 = 42
\]

#### Volume of the smaller prism:
\[
\text{Volume}_{\text{small}} = 5 \times 2 \times 2 = 20
\]

#### Total volume:
\[
\text{Total Volume} = 42 + 20 = 62
\]

Answer for Shape 3:
\[
\boxed{62}
\]

---

Shape 4:

This shape can be divided into two rectangular prisms:
1. A larger rectangular prism with dimensions \(6 \times 2 \times 4\).
2. A smaller rectangular prism with dimensions \(4 \times 2 \times 2\).

#### Volume of the larger prism:
\[
\text{Volume}_{\text{large}} = 6 \times 2 \times 4 = 48
\]

#### Volume of the smaller prism:
\[
\text{Volume}_{\text{small}} = 4 \times 2 \times 2 = 16
\]

#### Total volume:
\[
\text{Total Volume} = 48 + 16 = 64
\]

Answer for Shape 4:
\[
\boxed{64}
\]

---

Shape 5:

This shape can be divided into two rectangular prisms:
1. A larger rectangular prism with dimensions \(8 \times 2 \times 3\).
2. A smaller rectangular prism with dimensions \(6 \times 2 \times 2\).

#### Volume of the larger prism:
\[
\text{Volume}_{\text{large}} = 8 \times 2 \times 3 = 48
\]

#### Volume of the smaller prism:
\[
\text{Volume}_{\text{small}} = 6 \times 2 \times 2 = 24
\]

#### Total volume:
\[
\text{Total Volume} = 48 + 24 = 72
\]

Answer for Shape 5:
\[
\boxed{72}
\]

---

Shape 6:

This shape can be divided into two rectangular prisms:
1. A larger rectangular prism with dimensions \(9 \times 2 \times 3\).
2. A smaller rectangular prism with dimensions \(7 \times 2 \times 2\).

#### Volume of the larger prism:
\[
\text{Volume}_{\text{large}} = 9 \times 2 \times 3 = 54
\]

#### Volume of the smaller prism:
\[
\text{Volume}_{\text{small}} = 7 \times 2 \times 2 = 28
\]

#### Total volume:
\[
\text{Total Volume} = 54 + 28 = 82
\]

Answer for Shape 6:
\[
\boxed{82}
\]

---

Final Answers:

\[
\boxed{52, 63, 62, 64, 72, 82}
\]