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.

---

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 = $ \text{length} \times \text{width} \times \text{height} $
$$
V_1 = 9 \times 6 \times 3 = 162 \text{ m}^3
$$

#### 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 — let's check the diagram carefully:

Looking at the image:
- The bottom box has a height of 3 m, and the top box sits on it.
- The total height is 10 m, so the top box must have height = $10 - 3 = 7$ m?
But wait — the top box appears to be only 6 m long and 3 m wide, but the bottom box is 9 m long and 6 m wide.

Actually, from the diagram:
- The top prism is 6 m long, 3 m wide, and 7 m high? Wait — no.

Wait: The total height is 10 m, and the bottom prism is 3 m high → so the top prism must be 7 m high?

But that seems inconsistent with typical problems. Let’s double-check dimensions.

From the diagram:
- The bottom box: 9 m (length), 6 m (width), 3 m (height)
- The top box: 6 m (length), 3 m (width), and height is not labeled directly, but the total height is 10 m, and the bottom is 3 m → so the top box is 7 m high?

Wait — actually, look again: the top box is sitting on the bottom box, and the total height is 10 m. But the bottom box is only 3 m high, so the top box must be 7 m high?

That would make sense if the top box extends upward.

But wait — the top box has a depth of 3 m (same as width), and length of 6 m.

So:
- Top prism: 6 m × 3 m × 7 m → Volume = $6 \times 3 \times 7 = 126$ m³

But wait — the total height is 10 m, and the bottom is 3 m, so top is 7 m? That seems very tall compared to others.

Wait — perhaps I misread.

Let me re-analyze the labels:

- The bottom box is labeled: 9 m (length), 6 m (width), 3 m (height)
- The top box is labeled: 6 m (length), 3 m (width), and the total height of the whole figure is 10 m, so the top box must be 7 m high? But that doesn't seem right — unless it's correct.

Alternatively, maybe the top box is 7 m high, but that makes it taller than the bottom one.

But looking at the image: the top box is placed on the bottom box, and its height is not labeled. But the total height is 10 m, and the bottom box is 3 m high → so the top box is 7 m high.

So:
- Part 1 (Bottom): $9 \times 6 \times 3 = 162$ m³
- Part 2 (Top): $6 \times 3 \times 7 = 126$ m³

Total volume = $162 + 126 = 288$ m³

But wait — the top box is only 6 m long, but the bottom is 9 m long, so the top is centered? That’s fine.

But let's verify: is the top box really 7 m high?

Wait — look again: the total height is 10 m, and the bottom is 3 m → so top is 7 m high → yes.

So:
- Volume of part 1: $9 \times 6 \times 3 = 162$ m³
- Volume of part 2: $6 \times 3 \times 7 = 126$ m³
- Total: $162 + 126 = 288$ m³

✔ So answer for a is 288 m³

---

b.

This figure has three parts: a base, a middle box, and a top box.

But actually, it looks like two boxes:
- A long base (like a shelf) and a tall box on top.

Let’s label:

- Base: 8 m (length), 5 m (width), 1 m (height)
- Middle box: 6 m (length), 5 m (width), 7 m (height)? Wait — the height of the middle box is not clear.

Wait — the vertical side shows:
- The base is 1 m high
- Then a middle box is 6 m high? Wait — no.

Look at the vertical dimension: the total height is 7 m, and the base is 1 m → so the middle box is 6 m high?

But the middle box has length 6 m, width 5 m, height 6 m?

Wait — the base is 8 m long, 5 m wide, 1 m high → volume = $8 \times 5 \times 1 = 40$ m³

Then the middle box is 6 m long, 5 m wide, and height = ?

The total height is 7 m, and the base is 1 m → so the middle box is 6 m high.

But the middle box is placed on the base, and its length is 6 m, which is less than 8 m → okay.

So:
- Part 1 (Base): $8 \times 5 \times 1 = 40$ m³
- Part 2 (Middle): $6 \times 5 \times 6 = 180$ m³

Total volume = $40 + 180 = 220$ m³

Wait — but there's a third part? No, the middle box is 6 m high, and the base is 1 m → total height = 7 m → correct.

So total volume = 220 m³

✔ Answer for b: 220 m³

---

c.

This is a T-shaped figure.

It has:
- A horizontal base (like a shelf)
- A vertical column on top

But actually, it's a rectangular prism with a cutout or extension?

Wait — looking at the diagram:
- It's a vertical prism (11 cm high) with a horizontal extension at the bottom.

Dimensions:
- Vertical part: 4 cm (width), 3 cm (depth), 11 cm (height)
- Horizontal extension: 8 cm (length), 3 cm (depth), 4 cm (height)? Wait — no.

Wait — the horizontal part is 8 cm long, 3 cm deep, and 4 cm high? But the vertical part is 11 cm high, and the horizontal part is only 4 cm high? But they're connected.

Wait — the horizontal part is attached to the bottom of the vertical part.

From the diagram:
- The vertical part is 11 cm high, 4 cm wide, 3 cm deep
- The horizontal part is 8 cm long, 3 cm deep, and 4 cm high? But the depth is 3 cm for both.

Wait — the horizontal part has:
- Length = 8 cm
- Depth = 3 cm
- Height = 4 cm

But the vertical part has:
- Height = 11 cm
- Width = 4 cm
- Depth = 3 cm

And the horizontal part is attached to the side of the vertical part? Or is it underneath?

Actually, the horizontal part is attached at the bottom of the vertical part, extending outward.

But the vertical part is 11 cm high, and the horizontal part is only 4 cm high, so the vertical part extends above.

But the horizontal part is 8 cm long, 3 cm deep, 4 cm high → volume = $8 \times 3 \times 4 = 96$ cm³

The vertical part is 11 cm high, 4 cm wide, 3 cm deep → volume = $11 \times 4 \times 3 = 132$ cm³

But wait — do they overlap?

Yes — the vertical part is on top of the horizontal part, and they share the 4 cm × 3 cm area.

So the horizontal part is 8 cm long, 3 cm deep, 4 cm high → volume = $8 \times 3 \times 4 = 96$ cm³

The vertical part is 11 cm high, but only 4 cm wide, 3 cm deep, and it sits on top of the horizontal part → so it adds volume.

But the vertical part includes the 4 cm × 3 cm × 11 cm → but the bottom 4 cm overlaps with the horizontal part?

No — the horizontal part is only 4 cm high, and the vertical part is 11 cm high, so the vertical part is 11 cm high, but the horizontal part is only 4 cm high, so they are connected at the base.

So the vertical part has:
- Height = 11 cm
- Width = 4 cm
- Depth = 3 cm
→ Volume = $11 \times 4 \times 3 = 132$ cm³

The horizontal part is:
- Length = 8 cm
- Depth = 3 cm
- Height = 4 cm
→ Volume = $8 \times 3 \times 4 = 96$ cm³

But do they overlap in space?

Yes — the vertical part is on top of the horizontal part, so the bottom 4 cm of the vertical part is on the same base as the horizontal part.

But since they are solid, we don’t subtract — we just add the volumes.

Wait — but the horizontal part is 8 cm long, and the vertical part is 4 cm wide, so they are adjacent.

Actually, the horizontal part is 8 cm long, 3 cm deep, 4 cm high, and the vertical part is 4 cm wide, 3 cm deep, 11 cm high, and it is attached to the end of the horizontal part.

So they share a 4 cm × 3 cm face, but since it's solid, we just add the volumes.

So:
- Volume of horizontal part: $8 \times 3 \times 4 = 96$ cm³
- Volume of vertical part: $4 \times 3 \times 11 = 132$ cm³
- Total = $96 + 132 = 228$ cm³

✔ Answer for c: 228 cm³

---

d.

This is a rectangular prism with a hole or cutout.

The outer box is:
- Length = 12 m
- Width = 10 m
- Height = 9 m

But there is a rectangular cutout in the middle.

The cutout is:
- Length = 6 m
- Width = 2 m
- Height = 5 m

So we calculate:
- Volume of full box: $12 \times 10 \times 9 = 1080$ m³
- Volume of cutout: $6 \times 2 \times 5 = 60$ m³
- Volume of shape = $1080 - 60 = 1020$ m³

✔ Answer for d: 1020 m³

---

✔ Final Answers:

a.
- Volume of part 1: $9 \times 6 \times 3 = 162$ m³
- Volume of part 2: $6 \times 3 \times 7 = 126$ m³
- Total: $162 + 126 = \boxed{288}$ m³

b.
- Part 1 (base): $8 \times 5 \times 1 = 40$ m³
- Part 2 (middle): $6 \times 5 \times 6 = 180$ m³
- Total: $40 + 180 = \boxed{220}$ m³

c.
- Horizontal part: $8 \times 3 \times 4 = 96$ cm³
- Vertical part: $4 \times 3 \times 11 = 132$ cm³
- Total: $96 + 132 = \boxed{228}$ cm³

d.
- Full volume: $12 \times 10 \times 9 = 1080$ m³
- Cutout: $6 \times 2 \times 5 = 60$ m³
- Total: $1080 - 60 = \boxed{1020}$ m³

---

✔ Summary:

| Problem | Volume |
|--------|--------|
| a | 288 m³ |
| b | 220 m³ |
| c | 228 cm³ |
| d | 1020 m³ |

Let me know if you want this filled into the worksheet format!