Volume of Composite Figures worksheet with four 3D shapes to calculate total volume by breaking into parts.

Let’s solve each part step by step. We’ll find the volume of each composite figure by breaking it into two rectangular prisms (boxes), calculating their volumes separately, then adding them together.

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Part a:

The shape is made of two boxes stacked on top of each other.

- Top box:
Length = 6 m, Width = 3 m, Height = 3 m
Volume = 6 × 3 × 3 = 54 m³

- Bottom box:
Length = 9 m, Width = 6 m, Height = 6 m
Volume = 9 × 6 × 6 = 324 m³

Wait — let’s double-check the diagram. The bottom part is 9m long, 6m wide, and 6m high? But the total height from bottom to top is 9m, and the top part is 3m tall, so the bottom part must be 6m tall — that matches.

But look again: the top box sits on the bottom one, but its width is only 3m (not 6m). So yes, we’re correct.

Total volume = 54 + 324 = 378 m³

BUT — wait! Let me recheck the dimensions carefully.

Actually, looking at the labels:

- Bottom prism: length 9m, width 6m, height 6m → 9×6×6 = 324 m³ ✔
- Top prism: it’s sitting on the back half? Its length is 6m (same as bottom’s width?), no — actually, in the diagram, the top box has:
- Length = 6m (along the same direction as the 9m side? No — let's think differently.)

Actually, better way: The entire base is 9m x 6m. The bottom part is full size: 9m (length) × 6m (width) × 6m (height).

The top part is smaller: it’s 6m long (in the same direction as the 9m?), but only 3m wide (half the width), and 3m high.

Wait — perhaps the top box is 6m (length) × 3m (width) × 3m (height). Yes, that makes sense with the drawing.

So:

Volume of part 1 (top): 6 × 3 × 3 = 54 m³
Volume of part 2 (bottom): 9 × 6 × 6 = 324 m³
Total: 54 + 324 = 378 m³

✔ Correct.

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Part b:

This shape looks like an L-shape when viewed from front.

We can split it vertically or horizontally. Let’s split it into left and right parts.

Option 1: Split into a tall thin part on the left and a shorter wider part on the right.

Left part:
Width = 3m, Depth = 5m, Height = 6m → Volume = 3 × 5 × 6 = 90 m³

Right part:
It goes from x=3m to x=8m → width = 5m, depth = 5m, height = 7m? Wait — no.

Actually, looking at the diagram:

Total length along bottom is 8m. Left part is 3m wide, so right part is 5m wide.

Height of left part is 6m, height of right part is 7m? That doesn’t make sense — they should connect.

Wait — actually, the shape is like a step: the left part is taller? No — label says:

From left: 3m wide, 6m high. Then next section is 5m wide (since 3+5=8), and 7m high? But that would mean the right part is taller — possible.

But also, depth is 5m for both? Diagram shows “5m” labeled on the side — probably depth.

So:

Left prism: 3m (width) × 5m (depth) × 6m (height) = 90 m³
Right prism: 5m (width) × 5m (depth) × 7m (height) = 175 m³

Total = 90 + 175 = 265 m³

But wait — is the right part really 7m high? The diagram shows the overall height on the right is 7m, and left is 6m — so yes, it’s a stepped shape.

Alternatively, maybe we should split horizontally? But vertical split seems fine.

Another way: imagine the whole thing as a big box minus a missing part? But not necessary.

I think 90 + 175 = 265 m³ is correct.

But let me check units and labels again.

Diagram says:

- Bottom: 8m total length
- Left segment: 3m wide, 6m high
- Right segment: 5m wide (8-3), 7m high
- Depth: 5m (labeled on side)

Yes.

So:

Part 1 (left): 3 × 5 × 6 = 90
Part 2 (right): 5 × 5 × 7 = 175
Total: 265 m³

✔

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Part c:

This is a T-shaped or cross-shaped prism? Actually, it’s like a vertical bar with a horizontal base.

Split into two parts: the vertical column and the base platform.

Vertical part:
Width = 2cm, Depth = 4cm, Height = 11cm → Volume = 2 × 4 × 11 = 88 cm³

Base part:
It extends out on both sides. Total width of base is 5cm, but the vertical part is 2cm wide, so the base sticks out 1.5cm on each side? Not necessarily — let’s see labels.

Diagram shows:

- Vertical part: 2cm wide, 4cm deep, 11cm high
- Base: total width 5cm, depth 5cm, height 3cm? But the vertical part sits on top of the base.

Actually, the base is 5cm (width) × 5cm (depth) × 3cm (height) — but the vertical part is centered? Or attached?

Looking at the diagram: the base is 5cm wide and 5cm deep, and 3cm high. The vertical part is 2cm wide, 4cm deep, and 11cm high — but it sits on the base, so the total height is 11 + 3 = 14cm? But diagram says 11cm for the vertical part — probably including the base? No.

Label says: vertical part height is 11cm, and below it is a 3cm high base. So total height 14cm? But the 11cm might be just the upright part.

Actually, reading the diagram:

- The vertical rectangle is labeled 11cm high, 2cm wide, 4cm deep.
- Below it, there’s a base that is 5cm wide, 5cm deep, and 3cm high.
- Also, there’s a note: “3cm” between the vertical part and the edge — meaning the base extends 3cm beyond on one side? Since 5cm total width, and vertical part is 2cm wide, if centered, it would extend 1.5cm each side, but here it says “3cm” on one side — so probably not centered.

Actually, the diagram shows:

On the base: from left to right: 3cm, then the vertical part (2cm), then ? — total width 5cm, so 3 + 2 = 5, so no extension on the right? That means the vertical part is flush on the right.

Similarly, depth: vertical part is 4cm deep, base is 5cm deep — so extends 1cm in front or back.

But for volume, we don’t care about position, just sizes.

So:

Part 1 (vertical): 2 × 4 × 11 = 88 cm³
Part 2 (base): 5 × 5 × 3 = 75 cm³

Total = 88 + 75 = 163 cm³

Is that correct? The base is separate, and the vertical part is on top — so yes, we add them.

But is the vertical part sitting entirely on the base? In terms of volume, since they are solid and connected, we still add the volumes — no overlap because they are different parts.

Actually, if the vertical part is sitting on the base, and we count the base’s full volume and the vertical’s full volume, we are double-counting the area where they touch? No — because the vertical part starts above the base. The base is 3cm high, and the vertical part is 11cm high starting from the top of the base? Or is the 11cm including the base?

Looking at the diagram: the 11cm is labeled on the vertical part alone, and the 3cm is labeled on the base separately. Also, there’s a dimension showing the total height is 11cm + 3cm? Not explicitly, but likely the 11cm is the height of the upright section only.

In standard interpretation for such problems, the parts are non-overlapping.

So I think 88 + 75 = 163 cm³ is correct.

But let me confirm with another approach.

Imagine the whole shape: it’s like a base 5x5x3, and on top of it, a tower 2x4x11. Since the tower is placed on the base, and assuming no overlap in volume calculation (which is standard), we add.

Yes.

✔

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Part d:

This is a large box with a smaller box cut out or added? Looking at the diagram, it seems like a large rectangular prism with a smaller one attached or indented.

Actually, it looks like a main block and a smaller block sticking out on the side.

Labels:

Main block: 12m long, 5m wide, 9m high? But wait — the height is labeled 9m on the left, and on the right, there’s a smaller part that is 6m high.

Also, the smaller part is 4m long, 2m wide, 6m high? And it’s attached to the side.

Specifically:

- Main prism: length 12m, width 5m, height 9m → Volume = 12 × 5 × 9 = 540 m³

- Attached prism: it’s on the right end, protruding. Dimensions: length 4m (but is this additional or part of the 12m?).

Looking at the diagram: the total length is 12m for the main part, and the small part is attached to the side, so probably not extending the length.

Actually, the small part is on the face: it’s 4m in the direction perpendicular to the main length? Let’s read labels.

Diagram shows:

- Overall: 12m (length), 5m (width), 9m (height) for the main body.

- On the right side, there’s a smaller box that is 4m long (in the same direction as the 12m?), but that would make total length 16m — unlikely.

Perhaps the 4m is the depth or width.

Better: the small box is attached to the side, so it adds to the width or height.

Labels on small box: 4m, 2m, 6m.

And it’s positioned such that it sticks out from the main block.

Typically in such diagrams, the small box is attached to the face, so we add its volume.

Assume:

Main block: 12m × 5m × 9m = 540 m³

Small block: 4m × 2m × 6m = 48 m³

Total = 540 + 48 = 588 m³

But is the small block completely outside? Or is it carved out? The shading suggests it’s added, not removed.

In the diagram, the small part is shaded similarly, and it’s protruding, so likely added.

Moreover, the height of the small part is 6m, while main is 9m, so it’s shorter.

Also, the width: main is 5m, small is 2m — probably attached to the side.

So yes, additive.

Thus, total volume = 540 + 48 = 588 m³

✔

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Now, let’s write the answers as per the worksheet format.

For each part, fill in:

Volume of part 1: ___ × ___ × ___ = ___ m³
Volume of part 2: ___ × ___ × ___ = ___ m³
Volume of shape: ___ + ___ = ___ m³

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Final Answers:

a.
Volume of part 1: 6 × 3 × 3 = 54 m³
Volume of part 2: 9 × 6 × 6 = 324 m³
Volume of shape: 54 + 324 = 378 m³

b.
Volume of part 1: 3 × 5 × 6 = 90 m³
Volume of part 2: 5 × 5 × 7 = 175 m³
Volume of shape: 90 + 175 = 265 m³

c.
Volume of part 1: 2 × 4 × 11 = 88 cm³
Volume of part 2: 5 × 5 × 3 = 75 cm³
Volume of shape: 88 + 75 = 163 cm³

d.
Volume of part 1: 12 × 5 × 9 = 540 m³
Volume of part 2: 4 × 2 × 6 = 48 m³
Volume of shape: 540 + 48 = 588 m³

Note: For part c, units are cm³, others are m³ — as per diagram labels.

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Final Answer:
a. 378 m³
b. 265 m³
c. 163 cm³
d. 588 m³