Volume of Composite Figures Additive Volume - Worksheets - Free Printable

To solve the problem of finding the volume of each composite figure, we need to break down each shape into simpler geometric parts (like rectangular prisms), calculate the volume of each part, and then sum them up. Let's go through each part step by step.

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Part a:

The composite figure consists of two rectangular prisms stacked on top of each other.

#### Step 1: Identify the dimensions of each part.
- Part 1 (top prism):
- Length = 6 m
- Width = 3 m
- Height = 10 m

- Part 2 (bottom prism):
- Length = 9 m
- Width = 6 m
- Height = 9 m

#### Step 2: Calculate the volume of each part.
The formula for the volume of a rectangular prism is:
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

- Volume of Part 1:
\[
\text{Volume}_1 = 6 \, \text{m} \times 3 \, \text{m} \times 10 \, \text{m} = 180 \, \text{m}^3
\]

- Volume of Part 2:
\[
\text{Volume}_2 = 9 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m} = 486 \, \text{m}^3
\]

#### Step 3: Calculate the total volume.
\[
\text{Total Volume} = \text{Volume}_1 + \text{Volume}_2 = 180 \, \text{m}^3 + 486 \, \text{m}^3 = 666 \, \text{m}^3
\]

#### Final Answer for Part a:
\[
\boxed{666}
\]

---

Part b:

The composite figure consists of two rectangular prisms placed side by side.

#### Step 1: Identify the dimensions of each part.
- Part 1 (left prism):
- Length = 7 m
- Width = 3 m
- Height = 6 m

- Part 2 (right prism):
- Length = 8 m
- Width = 1 m
- Height = 5 m

#### Step 2: Calculate the volume of each part.
- Volume of Part 1:
\[
\text{Volume}_1 = 7 \, \text{m} \times 3 \, \text{m} \times 6 \, \text{m} = 126 \, \text{m}^3
\]

- Volume of Part 2:
\[
\text{Volume}_2 = 8 \, \text{m} \times 1 \, \text{m} \times 5 \, \text{m} = 40 \, \text{m}^3
\]

#### Step 3: Calculate the total volume.
\[
\text{Total Volume} = \text{Volume}_1 + \text{Volume}_2 = 126 \, \text{m}^3 + 40 \, \text{m}^3 = 166 \, \text{m}^3
\]

#### Final Answer for Part b:
\[
\boxed{166}
\]

---

Part c:

The composite figure consists of two rectangular prisms stacked on top of each other.

#### Step 1: Identify the dimensions of each part.
- Part 1 (top prism):
- Length = 5 cm
- Width = 3 cm
- Height = 2 cm

- Part 2 (bottom prism):
- Length = 5 cm
- Width = 3 cm
- Height = 11 cm

#### Step 2: Calculate the volume of each part.
- Volume of Part 1:
\[
\text{Volume}_1 = 5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} = 30 \, \text{cm}^3
\]

- Volume of Part 2:
\[
\text{Volume}_2 = 5 \, \text{cm} \times 3 \, \text{cm} \times 11 \, \text{cm} = 165 \, \text{cm}^3
\]

#### Step 3: Calculate the total volume.
\[
\text{Total Volume} = \text{Volume}_1 + \text{Volume}_2 = 30 \, \text{cm}^3 + 165 \, \text{cm}^3 = 195 \, \text{cm}^3
\]

#### Final Answer for Part c:
\[
\boxed{195}
\]

---

Part d:

The composite figure consists of a larger rectangular prism with a smaller rectangular prism removed from it.

#### Step 1: Identify the dimensions of the larger prism and the smaller prism.
- Larger Prism:
- Length = 12 m
- Width = 10 m
- Height = 7 m

- Smaller Prism (removed portion):
- Length = 6 m
- Width = 3 m
- Height = 5 m

#### Step 2: Calculate the volume of the larger prism.
\[
\text{Volume}_{\text{larger}} = 12 \, \text{m} \times 10 \, \text{m} \times 7 \, \text{m} = 840 \, \text{m}^3
\]

#### Step 3: Calculate the volume of the smaller prism.
\[
\text{Volume}_{\text{smaller}} = 6 \, \text{m} \times 3 \, \text{m} \times 5 \, \text{m} = 90 \, \text{m}^3
\]

#### Step 4: Calculate the total volume of the composite figure.
\[
\text{Total Volume} = \text{Volume}_{\text{larger}} - \text{Volume}_{\text{smaller}} = 840 \, \text{m}^3 - 90 \, \text{m}^3 = 750 \, \text{m}^3
\]

#### Final Answer for Part d:
\[
\boxed{750}
\]

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Final Answers:

\[
\boxed{666, 166, 195, 750}
\]