Volume of Composite Figures Additive Volume - Worksheets - Free Printable

Let's solve each composite figure step by step. These are all composite solids made up of two or more rectangular prisms (boxes). To find the total volume, we break each shape into simpler parts, calculate the volume of each part, and then add them together.

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a.

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

#### Part 1: Bottom prism
- Length = 9 m
- Width = 6 m
- Height = 3 m

Volume = length × width × height
= 9 × 6 × 3 = 162 m³

#### Part 2: Top prism
- Length = 9 m
- Width = 6 m
- Height = 7 m (since total height is 10 m, and bottom is 3 m → 10 − 3 = 7 m)

Wait — looking at the image carefully:
- The bottom prism has a height of 3 m, and the top prism sits on it with a total height of 10 m, so the top prism must be 7 m tall.
- But wait — the top prism appears to have same length and width as the bottom? Let's check:

Actually, from the diagram:
- The bottom block is 9 m × 6 m × 3 m → correct.
- The top block is 6 m wide, 6 m long, and 7 m high?

But the total height is labeled as 10 m, and the bottom block is 3 m, so the top block must be 7 m high.

But wait — the top block is only 6 m long, but the bottom is 9 m long. So the top block is smaller and centered?

So:

#### Part 1: Bottom prism
- L = 9 m, W = 6 m, H = 3 m
→ Volume = 9 × 6 × 3 = 162 m³

#### Part 2: Top prism
- L = 6 m, W = 6 m, H = 7 m
→ Volume = 6 × 6 × 7 = 252 m³

Wait! That can't be — the top block is only 6 m in length, but the height is 7 m? But the total height is 10 m, and bottom is 3 m → yes, top is 7 m high.

But let’s double-check the labels:

Looking at the image:
- The total height is 10 m.
- The bottom block is 3 m high.
- So the top block is 10 - 3 = 7 m high.
- The top block has dimensions: 6 m (length), 6 m (width), 7 m (height)

But the bottom block is 9 m long, 6 m wide, 3 m high

So:

✔ Volume of part 1: 9 × 6 × 3 = 162 m³
✔ Volume of part 2: 6 × 6 × 7 = 252 m³

Total volume = 162 + 252 = 414 m³

Wait — that seems large. Let's recheck the top block's length.

Wait — is the top block really 6 m long? Yes — it says 6 m along the front.

And the bottom is 9 m long.

Yes.

But let’s look again at the labeling: There’s a "3 m" next to the top block — is that the height or depth?

No — the vertical label is 10 m total, and 3 m is the bottom height.

So yes, top is 7 m high.

So:
- Part 1: 9 × 6 × 3 = 162 m³
- Part 2: 6 × 6 × 7 = 252 m³
- Total: 414 m³

But wait — this seems inconsistent with typical problems. Let's make sure we're not misreading.

Wait — actually, the top block might be 6 m long, 6 m wide, and 7 m high — but the bottom block is 9 m long, 6 m wide, 3 m high — so they’re both 6 m wide, but top is shorter in length.

Yes.

So:
- Volume of part 1: 9 × 6 × 3 = 162 m³
- Volume of part 2: 6 × 6 × 7 = 252 m³
- Total: 162 + 252 = 414 m³

But let’s see if the top block is actually not 7 m high.

Wait — the total height is 10 m, and the bottom block is 3 m, so top block is 7 m high — yes.

So final answer for a:

> Volume of part 1: 9 × 6 × 3 = 162 m³
> Volume of part 2: 6 × 6 × 7 = 252 m³
> Volume of shape: 162 + 252 = 414 m³

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b.

This is a step-like shape.

We can split it into two parts:
- A large rectangular prism at the base
- A smaller one on top

Let’s analyze:

From the image:
- The base is 8 m long, 6 m wide, and 3 m high (the lowest level)
- On top of that, there is a taller section: 5 m long, 6 m wide, 7 m high — but wait, the total height is 7 m, and the base is 3 m, so the top part is 4 m high?

Wait — the vertical dimension shows:
- From ground to bottom of top block: 3 m
- Then top block goes up to 7 m, so height of top block = 7 - 3 = 4 m

Also, the top block is 5 m long, 6 m wide, 4 m high

But the base is 8 m long, 6 m wide, 3 m high

Wait — but the top block is 5 m long, and the base is 8 m long — so the top block is placed on the back?

Let’s assume:
- Part 1 (bottom): 8 m × 6 m × 3 m = 144 m³
- Part 2 (top): 5 m × 6 m × 4 m = 120 m³

Total volume = 144 + 120 = 264 m³

But wait — the top block is 6 m wide, same as base, and 5 m long, and 4 m high

Yes.

So:
- Volume of part 1: 8 × 6 × 3 = 144 m³
- Volume of part 2: 5 × 6 × 4 = 120 m³
- Total: 264 m³

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c.

This is a rectangular prism with a smaller prism cut out? Or is it two parts?

Wait — no. It looks like a large vertical prism with a smaller one attached.

Wait — it's a T-shaped or L-shaped solid?

Actually, looking at the image:
- There is a large vertical prism: 11 cm high, 4 cm wide, 3 cm deep?
- And a horizontal prism extending from the bottom: 3 cm high, 4 cm wide, 5 cm long?

Wait — let's read the labels:

- The main vertical part: height = 11 cm, width = 4 cm, depth = 3 cm? Wait — no.

Wait — the horizontal part is 5 cm long, 3 cm high, 4 cm wide? But the vertical part is 11 cm high, 4 cm wide, 3 cm deep?

Actually, the entire figure is made of:
- A vertical rectangular prism: 11 cm high, 4 cm wide, 3 cm deep
- A horizontal rectangular prism attached at the bottom: 5 cm long, 3 cm high, 4 cm wide?

Wait — but the depth is 3 cm, and the width is 4 cm — confusing.

Wait — perhaps:
- The vertical part is: height = 11 cm, width = 4 cm, depth = 3 cm
- The horizontal part is: length = 5 cm, height = 3 cm, width = 4 cm — but this would mean it's attached at the bottom.

But the vertical part already has height 11 cm, and the horizontal part is 3 cm high, so it extends down?

No — probably the horizontal part is attached to the side.

Wait — better interpretation:

The figure has:
- A long horizontal prism at the bottom: 5 cm long, 3 cm high, 4 cm wide? But the vertical part is 11 cm high, 4 cm wide, 3 cm deep — so maybe the depth is 3 cm.

Let’s assume:
- The vertical prism is: 11 cm (height) × 4 cm (width) × 3 cm (depth) → volume = 11 × 4 × 3 = 132 cm³
- The horizontal prism is: 5 cm (length) × 3 cm (height) × 4 cm (width) → but wait, the height of the horizontal part is 3 cm, and it’s attached to the bottom of the vertical part?

But the vertical part is 11 cm high, so the horizontal part is 3 cm high, and 5 cm long, and 4 cm wide — but the depth is 3 cm?

Wait — the horizontal part is shown as 5 cm long, 3 cm high, and 4 cm wide — but the vertical part is 4 cm wide, 3 cm deep, 11 cm high

So likely:
- The vertical part is: 11 cm × 4 cm × 3 cm = 132 cm³
- The horizontal part is: 5 cm × 3 cm × 4 cm = 60 cm³

But wait — the horizontal part is 3 cm high, and the vertical part is 11 cm high, so if they are connected at the bottom, the horizontal part is 3 cm high, and the vertical part is 11 cm high, so the total height is 11 cm.

But the horizontal part is 5 cm long, 3 cm high, 4 cm wide

So total volume = 132 + 60 = 192 cm³

But wait — are they overlapping? No — the horizontal part is attached to the side of the vertical part?

Wait — actually, the horizontal part is attached to the bottom, and the vertical part is on top?

No — the vertical part is 11 cm high, and the horizontal part is 3 cm high, and they are joined at the bottom.

But the horizontal part is 5 cm long, and the vertical part is 4 cm wide, so likely the horizontal part is in front or to the side.

But since the depth is 3 cm for both, and width is 4 cm, it’s possible they are stacked.

Wait — the horizontal part is 3 cm high, and the vertical part is 11 cm high, so the vertical part is on top of the horizontal part?

But the horizontal part is 5 cm long, and the vertical part is 4 cm wide, so maybe the vertical part is on top of the horizontal part, but only over a portion.

Wait — this is ambiguous.

Wait — looking at the diagram:
- The vertical part is 11 cm high, 4 cm wide, 3 cm deep
- The horizontal part is 5 cm long, 3 cm high, 4 cm wide — but it's attached at the bottom of the vertical part?

But the vertical part is 11 cm high, and the horizontal part is 3 cm high, so the horizontal part is underneath the vertical part?

But the vertical part is 4 cm wide, and the horizontal part is 4 cm wide, so they match.

So:
- The vertical prism: 11 cm × 4 cm × 3 cm = 132 cm³
- The horizontal prism: 5 cm × 3 cm × 4 cm = 60 cm³

But do they overlap? Only in the 4 cm × 3 cm area.

But the horizontal prism is 5 cm long, and the vertical prism is 4 cm wide, so the overlap is 4 cm × 3 cm × 3 cm? No — the horizontal prism is 5 cm long, 3 cm high, 4 cm wide

The vertical prism is 11 cm high, 4 cm wide, 3 cm deep

So the vertical prism sits on top of the horizontal prism, and they share a 4 cm × 3 cm face.

But the horizontal prism is 5 cm long, so it extends 5 cm in one direction, while the vertical prism is 4 cm wide, so it fits within.

So no overlap in volume — they are separate in space.

But are they connected? Yes, but volume adds.

So total volume = 132 + 60 = 192 cm³

But wait — the horizontal prism is 3 cm high, and the vertical prism is 11 cm high, so the vertical prism extends 8 cm above the horizontal prism.

So yes — total volume = 132 + 60 = 192 cm³

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d.

This is a rectangular prism with a smaller prism removed.

From the image:
- The outer box is: 12 m long, 10 m wide, 5 m high → volume = 12 × 10 × 5 = 600 m³
- A smaller rectangular prism is cut out from it: 6 m long, 2 m wide, 5 m high? Wait — the depth is 5 m?

Wait — the cut-out is labeled: 6 m (length), 2 m (width), and the height is 5 m? But the outer box is 5 m high, so the cut-out is full height.

So:
- Volume of outer box: 12 × 10 × 5 = 600 m³
- Volume of cut-out: 6 × 2 × 5 = 60 m³
- Volume of shape = 600 − 60 = 540 m³

But wait — the cut-out is 6 m long, 2 m wide, 5 m high, and it's inside the larger box.

Yes — so subtract.

So:
- Volume of shape = 600 − 60 = 540 m³

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✔ Final Answers:

#### a.
- Volume of part 1: 9 × 6 × 3 = 162 m³
- Volume of part 2: 6 × 6 × 7 = 252 m³
- Volume of shape: 162 + 252 = 414 m³

#### b.
- Volume of part 1: 8 × 6 × 3 = 144 m³
- Volume of part 2: 5 × 6 × 4 = 120 m³
- Volume of shape: 144 + 120 = 264 m³

#### c.
- Volume of part 1: 11 × 4 × 3 = 132 cm³
- Volume of part 2: 5 × 3 × 4 = 60 cm³
- Volume of shape: 132 + 60 = 192 cm³

#### d.
- Volume of outer box: 12 × 10 × 5 = 600 m³
- Volume of cut-out: 6 × 2 × 5 = 60 m³
- Volume of shape: 600 − 60 = 540 m³

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✔ Final Answer Summary:

| Problem | Volume |
|--------|--------|
| a. | 414 m³ |
| b. | 264 m³ |
| c. | 192 cm³ |
| d. | 540 m³ |

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