Volume of Composite Figures Additive Volume - Worksheets - Free Printable

Let's solve the volume of composite figures problems step by step, based on the images you've provided.

We’ll go through each problem one at a time and calculate the volume using the formula for the volume of a rectangular prism:

> Volume = Length × Width × Height

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🔷 Problem 1: Volume of Composite Figure (Left Bottom)

This figure consists of two rectangular prisms stacked together:

#### Part 1: The bottom box
- Dimensions:
- Length = 9 m
- Width = 6 m
- Height = 6 m
- Volume = 9 × 6 × 6 = 324 m³

#### Part 2: The top box
- Dimensions:
- Length = 9 m
- Width = 6 m
- Height = 3 m
- Volume = 9 × 6 × 3 = 162 m³

#### Total Volume:
- Volume of shape = 324 + 162 = 486 m³

✔ Answer:
- Volume of part 1: 9 × 6 × 6 = 324 m³
- Volume of part 2: 9 × 6 × 3 = 162 m³
- Volume of shape: 324 + 162 = 486 m³

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🔷 Problem 2: Volume of the Building (Right Side)

This building is made of two rectangular parts.

#### Part 1: The taller section (left side)
- Dimensions:
- Length = 8 m
- Width = 4 m
- Height = 8 m
- Volume = 8 × 4 × 8 = 256 m³

#### Part 2: The shorter section (right side)
- Dimensions:
- Length = 6 m
- Width = 4 m
- Height = 4 m
- Volume = 6 × 4 × 4 = 96 m³

#### Total Volume:
- Total = 256 + 96 = 352 m³

✔ Answer:
- Volume of part 1: 8 × 4 × 8 = 256 m³
- Volume of part 2: 6 × 4 × 4 = 96 m³
- Volume of building: 256 + 96 = 352 m³

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🔷 Problem 3: Volume of Composite Figure (Top Left – "a")

This figure looks like an L-shaped solid. We can break it into two rectangles.

Let’s analyze:

We have:
- A vertical part: 6 m high, 4 m wide, 5 m deep
- A horizontal part: 3 m high, 9 m long, 5 m deep

But let's be careful — we need to avoid double-counting overlapping parts.

Actually, better to split it into two non-overlapping boxes.

#### Option: Split into two rectangles

##### Rectangle 1: The back (taller) part
- Dimensions:
- Length = 4 m
- Width = 5 m
- Height = 6 m
- Volume = 4 × 5 × 6 = 120 m³

##### Rectangle 2: The front (shorter) part
- Dimensions:
- Length = 9 m – 4 m = 5 m (since 4 m is already taken)
- Width = 5 m
- Height = 3 m
- Volume = 5 × 5 × 3 = 75 m³

Wait — but look at the diagram again: total length is 9 m, and the front part extends 5 m in depth.

Actually, looking carefully:

The entire base is 9 m long and 5 m deep.

But the height varies:
- On the left: 6 m tall (4 m width)
- On the right: 3 m tall (5 m width)

So yes:

#### Part 1: Left block
- L = 4 m, W = 5 m, H = 6 m → 4 × 5 × 6 = 120 m³

#### Part 2: Right block
- L = 5 m (9 − 4), W = 5 m, H = 3 m → 5 × 5 × 3 = 75 m³

Total volume = 120 + 75 = 195 m³

✔ Answer:
- Volume of part 1: 4 × 5 × 6 = 120 m³
- Volume of part 2: 5 × 5 × 3 = 75 m³
- Volume of shape: 120 + 75 = 195 m³

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🔷 Problem 4: Volume of Composite Figure (Top Left – "b")

This is a rectangular prism with a smaller prism removed from the corner.

It looks like a large box with a smaller box cut out.

#### Step 1: Volume of the big box
- L = 10 cm, W = 9 cm, H = 5 cm
- Volume = 10 × 9 × 5 = 450 cm³

#### Step 2: Volume of the removed part
- L = 7 cm, W = 2 cm, H = 6 cm
- Volume = 7 × 2 × 6 = 84 cm³

#### Final Volume:
- Total = 450 − 84 = 366 cm³

✔ Answer:
- Volume of big box: 10 × 9 × 5 = 450 cm³
- Volume of removed part: 7 × 2 × 6 = 84 cm³
- Volume of shape: 450 − 84 = 366 cm³

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✔ Summary of All Answers

| Problem | Volume |
|--------|--------|
| Bottom-left (stacked) | 486 m³ |
| Building (right) | 352 m³ |
| Top-left (L-shape) | 195 m³ |
| Top-left (cut-out) | 366 cm³ |

Let me know if you’d like these answers formatted for printing or explanation in simpler terms!