Find the volume of each L-block in this math worksheet.

Let's solve each of the L-block volume problems step by step.

The volume of a rectangular prism is given by:

$$
\text{Volume} = \text{length} \times \text{width} \times \text{height}
$$

Each L-shaped block can be broken into two rectangular prisms, and we calculate the volume of each part, then add them together.

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1)

Dimensions:
- Left vertical part: 10 mm (height), 8 mm (width), 2 mm (depth)
- Right horizontal part: 3 mm (height), 4 mm (width), 2 mm (depth)

Wait — let’s look carefully. The total length is 12 mm, and the horizontal part is 8 mm long? Actually, from the diagram:

- The vertical part: height = 10 mm, width = 8 mm, depth = 2 mm → Volume = $10 \times 8 \times 2 = 160$ mm³
- The horizontal part: height = 3 mm, width = (12 - 8) = 4 mm, depth = 2 mm → Volume = $3 \times 4 \times 2 = 24$ mm³

But wait — actually, the horizontal part is 8 mm in length and 3 mm high, but it's only 4 mm wide?

Wait — looking again: the total base is 12 mm, and the vertical part is 8 mm wide, so the horizontal extension is $12 - 8 = 4$ mm? But the horizontal part shows 8 mm labeled.

Actually, let’s interpret the diagram properly.

From the drawing:
- The vertical block is 10 mm tall, 8 mm wide, and 2 mm deep.
- The horizontal block is 3 mm tall, 4 mm wide, and 2 mm deep?
No — the horizontal part extends from the bottom, and its length is 12 mm, but the vertical part is only 8 mm long, so the horizontal part must extend 4 mm beyond?

Wait — better to think: the entire base is 12 mm long, and the vertical block is 8 mm wide, so the horizontal block is 12 mm long, but only 3 mm high, and 2 mm deep.

But the horizontal part is shown with a 3 mm height, and 8 mm width? Wait — no, the label says "8 mm" on the top of the horizontal section.

Actually, re-examining:

Looking at the figure:

- The bottom horizontal part has:
- Length = 12 mm
- Height = 3 mm
- Depth = 2 mm
- The vertical part sits on top of this, extending up:
- It is 10 mm tall (so 7 mm above the horizontal part)
- Width = 8 mm (overlapping with the horizontal part)
- Depth = 2 mm

So the vertical block is: $10 \times 8 \times 2 = 160$ mm³
But the horizontal block is: $3 \times 12 \times 2 = 72$ mm³

But now we have overlap: the part where they meet is counted twice.

So better approach: break the L-shape into two non-overlapping rectangles.

Better method: divide the L-shape into two rectangles that don't overlap.

For example:

- Vertical rectangle: 10 mm × 8 mm × 2 mm → $10 \times 8 \times 2 = 160$
- Horizontal rectangle: 3 mm × (12 - 8) = 4 mm × 2 mm → $3 \times 4 \times 2 = 24$

Wait — no. The horizontal part is not just 4 mm. The horizontal part goes all the way across 12 mm, but only 3 mm high, and the vertical part is on top of the first 8 mm.

So the entire shape consists of:

1. A rectangular prism for the base: 12 mm (length) × 3 mm (height) × 2 mm (depth) → $12 \times 3 \times 2 = 72$ mm³
2. A top piece: 8 mm (width) × (10 - 3) = 7 mm (height) × 2 mm (depth) → $8 \times 7 \times 2 = 112$ mm³

Total volume = $72 + 112 = 184$ mm³

✔ Answer: 184 mm³

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2)

Units: feet

- Vertical part: 16 ft (height), 4 ft (width), 5 ft (depth)? Wait, dimensions:
- Bottom horizontal: 5 ft (length), 4 ft (height), 8 ft (width)? No.

From diagram:

- Horizontal part: 5 ft (depth), 4 ft (height), 8 ft (width)
- Vertical part: 16 ft (height), 4 ft (width), 5 ft (depth)

Wait — both parts share the same depth = 5 ft.

But the horizontal part has width = 8 ft, height = 4 ft, depth = 5 ft → Volume = $8 \times 4 \times 5 = 160$ ft³
Vertical part: width = 4 ft, height = (16 - 4) = 12 ft? No — the vertical part is 16 ft tall, but the horizontal part is 4 ft high, so the vertical part extends 12 ft above.

But the vertical part is attached to the end of the horizontal part.

So:

- Horizontal block: $8 \times 4 \times 5 = 160$ ft³
- Vertical block: $4 \times 12 \times 5 = 240$ ft³
- Total = $160 + 240 = 400$ ft³

But wait — the vertical block has width = 4 ft, height = 16 ft, depth = 5 ft → $4 \times 16 \times 5 = 320$ ft³
But the horizontal block is 8 ft long, 4 ft high, 5 ft deep → $8 \times 4 \times 5 = 160$ ft³

Now, do they overlap? Yes — the vertical block is attached to the end of the horizontal block, so their shared region is 4 ft (width) × 4 ft (height) × 5 ft (depth) → $4 \times 4 \times 5 = 80$ ft³

But if we just add 320 + 160 = 480, we double-count the overlap.

So correct way: split into non-overlapping parts.

Better: split as:

- Bottom horizontal: 8 ft (length) × 4 ft (height) × 5 ft (depth) → $8 \times 4 \times 5 = 160$
- Top vertical: 4 ft (width) × (16 - 4) = 12 ft (height) × 5 ft (depth) → $4 \times 12 \times 5 = 240$

But the vertical part is only 4 ft wide, not 8 ft. So the total is:

- Horizontal: 8×4×5 = 160
- Vertical: 4×12×5 = 240
- Total = 160 + 240 = 400 ft³

✔ Answer: 400 ft³

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3)

Units: cm

Shape: L-shaped, with:

- Bottom: 9 cm (length), 5 cm (height), 3 cm (depth)
- Top: 1 cm (height), 2 cm (width), 3 cm (depth)

Wait — the top is 1 cm high, and the bottom is 5 cm high? But the total height is 5 cm, so the top is on top of the bottom.

From diagram:

- Bottom block: length = 9 cm, height = 5 cm, depth = 3 cm → $9 \times 5 \times 3 = 135$ cm³
- Top block: width = 2 cm, height = 1 cm, depth = 3 cm → $2 \times 1 \times 3 = 6$ cm³

But are they overlapping? The top block is placed on top of the left side of the bottom block, so no overlap.

Wait — the top block is shorter in length — only 2 cm, and it's on top of the left end.

So total volume = $135 + 6 = 141$ cm³

But wait — the total height is 5 cm, and the top block adds only 1 cm, so the bottom is 5 cm high, top is 1 cm high? That would make total height 6 cm, but it's labeled 5 cm.

Ah! Look: the total height is 5 cm, and the top block is 1 cm high, so the bottom block is only 4 cm high?

Wait — the diagram shows:

- The bottom block: height = 5 cm? But the top block is added on top, and it's 1 cm high.

But the total height is 5 cm — so the bottom block is 4 cm high, and the top block is 1 cm high?

Wait — the side view shows:

- Bottom part: 5 cm height
- Top part: 1 cm height — so total height = 6 cm?

But the label says "5 cm" on the side.

Wait — the side is labeled "5 cm", which is the depth.

Re-read: the side says "5 cm" — likely depth.

Look: the block has:

- Depth = 3 cm (front)
- Height = 5 cm (side)
- But the top has a smaller piece.

Actually, the total height is 5 cm, and the top block is 1 cm high, so the bottom block is 4 cm high.

But the bottom block is 9 cm long, 5 cm high? No — the total height is 5 cm, and the top block is 1 cm high, so the bottom block is 4 cm high.

Wait — the diagram shows:

- Bottom block: height = 4 cm? But labeled "5 cm" on the side.

Wait — the label "5 cm" is on the depth, i.e., front-to-back.

So:

- Depth = 3 cm (front), 5 cm (side)? No — the label "5 cm" is on the side, so it's the height.

Wait — confusion.

Let’s analyze:

- The vertical side is labeled "5 cm" — so height = 5 cm
- The top small block is labeled "1 cm" — so it's 1 cm high
- But if the whole thing is 5 cm high, and the top block is 1 cm, then the bottom block is 4 cm high?

But the bottom block is shown to go up to full height.

Wait — perhaps the top block is 1 cm high, and the bottom block is 5 cm high — but then total height would be 6 cm, which contradicts.

Unless the top block is inset.

Wait — the diagram shows:

- The main body: 9 cm long, 5 cm high, 3 cm deep
- On top, a smaller block: 2 cm wide, 1 cm high, 3 cm deep — but it's on the left end, and the total height is 5 cm, so the bottom block is 5 cm high, and the top block is additional 1 cm, making total height 6 cm?

But the side is labeled "5 cm".

Wait — the side is labeled "5 cm" — probably the depth.

Let’s assume:

- The depth (front-to-back) is 3 cm
- The height (vertical) is 5 cm
- The length is 9 cm

But the top block is 1 cm high, and it's placed on top of the left end.

So:

- Bottom block: 9 cm (length) × 5 cm (height) × 3 cm (depth) → $9 \times 5 \times 3 = 135$ cm³
- Top block: 2 cm (width) × 1 cm (height) × 3 cm (depth) → $2 \times 1 \times 3 = 6$ cm³

But the top block is on top of the bottom block, so it doesn’t increase height — it’s already included.

Wait — the bottom block is 5 cm high, and the top block is 1 cm high — but that would make total height 6 cm.

But the side is labeled "5 cm" — so maybe the top block is 1 cm high, and the bottom block is 4 cm high?

Yes — likely.

So:

- Bottom block: length = 9 cm, height = 4 cm, depth = 3 cm → $9 \times 4 \times 3 = 108$ cm³
- Top block: length = 2 cm, height = 1 cm, depth = 3 cm → $2 \times 1 \times 3 = 6$ cm³
- Total = $108 + 6 = 114$ cm³

But the top block is placed on the left end, and the bottom block is 9 cm long, so yes.

Alternatively, the top block might be 2 cm wide and 1 cm high, and the bottom block is 9 cm long, 5 cm high, 3 cm deep — but then the top block is on top, so total height = 6 cm, but the label says 5 cm.

So contradiction.

Wait — the side is labeled "5 cm" — but it's the depth.

Looking at the diagram:

- The side edge is labeled "5 cm" — this is the depth (front to back)
- The height is labeled "1 cm" on the top block, and "5 cm" on the main body? No — the main body has no height label.

Wait — the vertical side is labeled "5 cm" — that's likely the height.

But the top block is 1 cm high, so if the main block is 5 cm high, total height is 6 cm.

But the diagram shows the total height as 5 cm — so the top block is 1 cm high, and the main block is 4 cm high.

So:

- Main block: 9 cm (length) × 4 cm (height) × 3 cm (depth) → $9 \times 4 \times 3 = 108$
- Top block: 2 cm (width) × 1 cm (height) × 3 cm (depth) → $2 \times 1 \times 3 = 6$
- Total = $108 + 6 = 114$ cm³

✔ Answer: 114 cm³

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This is taking too long — let's do a systematic approach for all.

We'll go one by one.

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1)

Break into:
- Base: 12 mm × 3 mm × 2 mm = $12 \times 3 \times 2 = 72$ mm³
- Top: 8 mm × (10 - 3) = 7 mm × 2 mm = $8 \times 7 \times 2 = 112$ mm³
- Total = $72 + 112 = 184$ mm³ ✔

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2)

- Horizontal: 8 ft × 4 ft × 5 ft = $8 \times 4 \times 5 = 160$ ft³
- Vertical: 4 ft × (16 - 4) = 12 ft × 5 ft = $4 \times 12 \times 5 = 240$ ft³
- Total = $160 + 240 = 400$ ft³ ✔

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3)

- Bottom: 9 cm × 4 cm × 3 cm = $9 \times 4 \times 3 = 108$ cm³ (since total height is 5 cm, top is 1 cm, so bottom is 4 cm)
- Top: 2 cm × 1 cm × 3 cm = $2 \times 1 \times 3 = 6$ cm³
- Total = $108 + 6 = 114$ cm³ ✔

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4)

Dimensions:
- Lower block: 12 in × 4 in × 10 in = $12 \times 4 \times 10 = 480$ in³
- Upper block: 3 in × 5 in × 10 in = $3 \times 5 \times 10 = 150$ in³
- Total = $480 + 150 = 630$ in³ ✔

Note: The upper block is on top of the lower block, and they share the same depth (10 in), and the upper block is 3 in high, lower is 4 in high, so total height = 7 in.

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5)

L-shaped, lying horizontally.

- Long horizontal part: 15 m × 4 m × 11 m = $15 \times 4 \times 11 = 660$ m³
- Short vertical part: 2 m × 5 m × 11 m = $2 \times 5 \times 11 = 110$ m³
- Total = $660 + 110 = 770$ m³ ✔

Wait — check: the short part is 2 m high, 5 m wide, 11 m deep — yes.

And the long part is 15 m long, 4 m high, 11 m deep.

They are connected — no overlap.

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6)

L-shaped, standing upright.

- Vertical part: 16 cm × 2 cm × 8 cm = $16 \times 2 \times 8 = 256$ cm³
- Horizontal part: 3 cm × 5 cm × 8 cm = $3 \times 5 \times 8 = 120$ cm³
- Total = $256 + 120 = 376$ cm³ ✔

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7)

L-shaped, lying flat.

- Long horizontal: 11 ft × 2 ft × 3 ft = $11 \times 2 \times 3 = 66$ ft³
- Vertical part: 6 ft × 5 ft × 3 ft = $6 \times 5 \times 3 = 90$ ft³
- Total = $66 + 90 = 156$ ft³ ✔

Wait — the vertical part is 6 ft long, 5 ft high, 3 ft deep.

The horizontal part is 11 ft long, 2 ft high, 3 ft deep.

They are joined — no overlap.

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8)

This is an open channel shape — like a U, but open.

It's made of three rectangles?

Wait — it looks like a U-shaped block.

Dimensions:
- Outer: 18 in (length), 12 in (height), 6 in (depth)
- Inner: 18 in (length), 5 in (height), 6 in (depth) — but it's cut out?

Wait — no — it's a solid L-shape? No — it's a channel.

But the problem says "L-blocks", so maybe it's a solid.

Looking: it has three parts? Or two?

Actually, it's a U-shape, but the diagram shows two arms.

Wait — it's an L-shaped block with a cutout?

No — the diagram shows a solid shape.

Wait — it's a double-L or U shape.

But the problem says "L-block", so likely it's a solid.

But the figure shows:

- Two arms: one 12 in high, 6 in wide, 6 in deep
- Another arm: 18 in long, 5 in high, 6 in deep

Wait — it's a U-shaped block with:
- Two vertical sides: 12 in high, 6 in wide, 6 in deep
- One horizontal bottom: 18 in long, 5 in high, 6 in deep

But the bottom is only 5 in high, and the sides are 12 in high.

But the total height is 12 in.

So volume = volume of two vertical walls + volume of bottom

But the bottom is 18 in long, 5 in high, 6 in deep

Each vertical wall: 12 in high, 6 in wide, 6 in deep

But the bottom is shared.

So:

- Left wall: $12 \times 6 \times 6 = 432$ in³
- Right wall: $12 \times 6 \times 6 = 432$ in³
- Bottom: $18 \times 5 \times 6 = 540$ in³
- Total = $432 + 432 + 540 = 1404$ in³

But wait — the bottom is only 5 in high, and the walls are 12 in high, so the walls extend 7 in above the bottom.

But the bottom is 18 in long, and the walls are 6 in wide.

But the gap between walls is 18 - 6 - 6 = 6 in?

Wait — the bottom is 18 in long, and the walls are on both ends.

So:

- Left wall: 12 in high, 6 in wide, 6 in deep
- Right wall: 12 in high, 6 in wide, 6 in deep
- Bottom: 18 in long, 5 in high, 6 in deep

But the bottom is only 5 in high, so the walls are 7 in higher than the bottom.

But the total height is 12 in.

So the volume is:

- Left wall: $12 \times 6 \times 6 = 432$
- Right wall: $12 \times 6 \times 6 = 432$
- Bottom: $18 \times 5 \times 6 = 540$
- Total = $432 + 432 + 540 = 1404$ in³

But is there overlap? No — the walls are on the ends, and the bottom is in the middle.

But the bottom is only 5 in high, and the walls are 12 in high, so they are separate.

Yes.

But the bottom is 18 in long, so it connects the two walls.

So total volume = $432 + 432 + 540 = 1404$ in³ ✔

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9)

L-shaped, with:
- Bottom: 13 m × 7 m × 6 m = $13 \times 7 \times 6 = 546$ m³
- Top: 4 m × 4 m × 6 m = $4 \times 4 \times 6 = 96$ m³
- Total = $546 + 96 = 642$ m³

Wait — the top is 4 m high, and the bottom is 7 m high, so total height = 11 m, which matches the label.

But the top is only 4 m wide, and the bottom is 13 m long.

So:

- Bottom block: 13 m (length) × 7 m (height) × 6 m (depth) = $13 \times 7 \times 6 = 546$
- Top block: 4 m (width) × 4 m (height) × 6 m (depth) = $4 \times 4 \times 6 = 96$
- Total = $546 + 96 = 642$ m³ ✔

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Final Answers:

| # | Volume |
|---|--------|
| 1 | 184 mm³ |
| 2 | 400 ft³ |
| 3 | 114 cm³ |
| 4 | 630 in³ |
| 5 | 770 m³ |
| 6 | 376 cm³ |
| 7 | 156 ft³ |
| 8 | 1404 in³ |
| 9 | 642 m³ |

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✔ All solved.