Educational math worksheet for calculating the volume of composite figures and buildings.

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 prisms joined together.

Let’s break it down:

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

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

⚠️ Wait! Let's double-check the width.
From the diagram, both buildings appear to be connected along the width, but the depth (width) seems consistent as 4 m.

But look carefully: the right building has a length of 6 m and height of 4 m, and depth of 4 m? Yes — it's attached to the left building, so depth should match.

So yes, dimensions are correct.

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

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

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

This figure looks like an L-shaped solid, which can be split into two rectangles.

Let’s analyze:

#### Part 1: Front-left vertical block
- Dimensions:
- Length = 6 m
- Width = 4 m
- Height = 5 m
- Volume = 6 × 4 × 5 = 120 m³

Wait — let's check again.

Looking closely at the diagram:

The entire base is 9 m long, with a step in the middle.

It appears this is composed of:

#### Part 1: The front lower rectangle
- Dimensions:
- Length = 9 m
- Width = 3 m
- Height = 3 m
- Volume = 9 × 3 × 3 = 81 m³

#### Part 2: The back upper rectangle
- Dimensions:
- Length = 4 m
- Width = 6 m
- Height = 5 m
- Volume = 4 × 6 × 5 = 120 m³

Wait — but the total length is 9 m, and the front part is 4 m wide?

Actually, looking more carefully:

Let me re-analyze:

The figure has:
- A base that is 9 m long and 3 m high.
- On top of that, there's a rectangular block that is 4 m long, 6 m wide, and 5 m tall.

But wait — the height of the whole figure is 8 m on the left side, and 5 m on the right?

Wait — labels:

- Left side: 8 m (total height), 6 m (top height), 5 m (bottom height) → So the bottom block is 5 m high?
- But then the top block is 6 m high?

Wait — this is confusing.

Let’s label clearly:

From the diagram:

- The entire base is 9 m long, 4 m wide, and 3 m high? No.

Wait — actually, from the image:

Labeling:

- The lower part is:
- Length = 9 m
- Width = 4 m
- Height = 3 m

- The upper part is:
- Length = 6 m
- Width = 4 m
- Height = 5 m

But wait — the total height on the left is 8 m, and the upper block is only 5 m high? That doesn't add up.

Wait — the left side shows:

- From bottom to top: 3 m (bottom) + 5 m (top) = 8 m → So yes!

So the bottom block is 3 m high, and the top block is 5 m high.

Now, what about the width?

The bottom block is 9 m long, 4 m wide, 3 m high → Volume = 9 × 4 × 3 = 108 m³

The top block is 6 m long, 4 m wide, 5 m high → Volume = 6 × 4 × 5 = 120 m³

Wait — but the top block sits on the back part?

No — actually, from the diagram:

- The top block is not sitting on the full 9 m base — it's only 6 m long and sits on the back part?

But the width is 4 m for both?

Wait — no. Actually, the width might be different.

Wait — let's read the labels:

- The front face shows:
- Left side: 8 m total height
- Bottom: 3 m
- Top: 5 m
- Depth (width): 4 m
- Length: 9 m

And the top block is 6 m long, 4 m deep, 5 m high

So:

#### Part 1: Bottom block
- Length = 9 m
- Width = 4 m
- Height = 3 m
- Volume = 9 × 4 × 3 = 108 m³

#### Part 2: Top block
- Length = 6 m
- Width = 4 m
- Height = 5 m
- Volume = 6 × 4 × 5 = 120 m³

Total volume = 108 + 120 = 228 m³

✔ Answer:
- Volume of part 1: 9 × 4 × 3 = 108 m³
- Volume of part 2: 6 × 4 × 5 = 120 m³
- Volume of shape: 108 + 120 = 228 m³

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🔷 Problem 4: Volume of Composite Figure (Top Right)

This is a rectangular prism with a cut-out.

Dimensions of the large box:
- Length = 10 cm
- Width = 7 cm
- Height = 5 cm

But there's a smaller rectangular prism removed from the corner.

The cut-out:
- Length = 6 cm
- Width = 2 cm
- Height = 5 cm

Wait — is the cut-out inside or on top?

From the diagram:
- It's a hole cut out from the side, going through the depth.

But the height is 5 cm, same as the big box, so it goes all the way through.

So we subtract the volume of the cut-out.

#### Volume of big box:
- 10 × 7 × 5 = 350 cm³

#### Volume of cut-out:
- 6 × 2 × 5 = 60 cm³

#### Net volume:
- 350 − 60 = 290 cm³

✔ Answer:
- Volume of solid = 350 − 60 = 290 cm³

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## ✔ Final Answers Summary:

1. Bottom Left Figure (Stacked):

- Part 1: 9 × 6 × 6 = 324 m³
- Part 2: 9 × 6 × 3 = 162 m³
- Total: 486 m³

2. Building (Right Side):

- Part 1: 8 × 4 × 8 = 256 m³
- Part 2: 6 × 4 × 4 = 96 m³
- Total: 352 m³

3. Top Left L-Shaped Figure:

- Part 1: 9 × 4 × 3 = 108 m³
- Part 2: 6 × 4 × 5 = 120 m³
- Total: 228 m³

4. Top Right Box with Cut-Out:

- Big box: 10 × 7 × 5 = 350 cm³
- Cut-out: 6 × 2 × 5 = 60 cm³
- Total: 290 cm³

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Let me know if you'd like these written neatly for a worksheet!