Count the cubes to find the volume of each 3D shape in this math worksheet.

Let's solve each of the 3D shapes by counting the number of individual cubes in each figure. The volume is simply the total number of unit cubes that make up each shape.

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1)

This shape has:
- A base of 2 cubes.
- One cube stacked on top of one of them.
- Another cube stacked on top of that (so a tower of 3).
- And one more cube next to the base.

Let’s break it down:
- Bottom layer: 3 cubes (two side-by-side, and one extending forward)
- Middle layer: 1 cube
- Top layer: 1 cube

Wait — let’s look carefully.

Actually, it looks like:
- Front row: 1 cube at bottom, 1 above it → 2 cubes
- Back row: 2 cubes at bottom, and 1 cube stacked on top of the back one → 3 cubes

Wait — better approach: count all visible and hidden cubes.

Looking closely:
- The structure has:
- 3 cubes in the back column (stacked vertically).
- 2 cubes in the front row (side-by-side).
- But the front left cube is directly in front of the bottom back cube.

So:
- Bottom layer: 3 cubes (2 in back, 1 in front-left)
- Middle layer: 1 cube (on top of the back-left cube)
- Top layer: 1 cube (on top of that)

Wait — no:

Actually, from the image:
- There are 3 cubes in the vertical stack (back right).
- Then, to the left of that, there are two cubes at the bottom (one in front, one behind), forming a horizontal line.
- But the front one is not stacked.

Better: Count all cubes.

Visualize:
- Layer 1 (bottom): 3 cubes (left-back, right-back, and front-right? Wait...)

Actually, standard way: use layers.

Let’s do it systematically.

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Instead, here's a clearer method: count all cubes, including those hidden.

We’ll go through each one.

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1)

Shape: L-shaped with a vertical stack.

Break into parts:
- Base: 3 cubes (in an L-shape: two in a row, one sticking out)
- On top of the corner cube: 2 more cubes stacked

So:
- Bottom: 3 cubes
- Middle: 1 cube (on top of one of the bottom ones)
- Top: 1 cube

Total = 3 + 1 + 1 = 5 cubes

✔ Volume: 5 cubes

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2)

A straight vertical tower of 4 cubes.

Each cube stacked on top of the other.

✔ Volume: 4 cubes

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3)

A 2×2×2 cube (like a small cube made of smaller cubes).

It's a cube with 2 cubes along each edge.

So: 2 × 2 × 2 = 8 cubes

✔ Volume: 8 cubes

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4)

Looks like a 2×2 square base, but one cube missing?

Wait: it's a 2×2×2 block, but with one cube removed?

No — actually, it's a 3D "L" shape.

From the drawing:
- Bottom layer: 3 cubes (a 2×2 square minus one corner)
- Top layer: 1 cube on top of one of the bottom cubes

Wait — no, it's actually:

- Two cubes in the back row (stacked vertically)
- One cube in front of the left one
- One cube in front of the right one?

Wait — better: it’s a 2×2×2 block missing one cube?

No — looking at it:

It appears to be:
- 4 cubes in total: a 2×2 square on the bottom, and one cube on top of the back-left one?

Wait — no.

Actually, this is a 2×2×2 cube with one cube missing? No.

Wait — let's count:

- Bottom layer: 3 cubes (front-left, front-right, back-left)
- Top layer: 1 cube (on top of back-left)

So total: 3 + 1 = 4 cubes

But wait — if it's a 2×2 base, that’s 4 cubes, but only 3 are shown? No.

Actually, this shape is not full.

Looking at the drawing:
- It's a 2×2 square base, but only 3 cubes are visible?
No — actually, it's a 3D shape where:
- Left column: 2 cubes high
- Right column: 1 cube high
- Front row: 1 cube (attached to the left column)

Wait — perhaps it's:

- Bottom: 3 cubes (left-front, left-back, right-back)
- Top: 1 cube on top of left-back

That makes 4 cubes.

Yes.

Alternatively: think of it as a 2×2×2 cube missing the front-right cube?

No — because the front-right cube isn't there.

So:
- Left column: 2 cubes (bottom and top)
- Back row: 2 cubes (bottom and top)
- But the front-right cube is missing.

Wait — no, the drawing shows:

- Bottom: 3 cubes: front-left, back-left, back-right
- Top: 1 cube on top of back-left

So total = 4 cubes.

✔ Volume: 4 cubes

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5)

A rectangular prism: 2 cubes wide, 2 cubes deep, 3 cubes tall.

So: 2 × 2 × 3 = 12 cubes

But wait — check: it’s a solid block?

Yes — it looks like a solid rectangle: 2 columns, each 3 cubes high, and 2 rows deep.

So: 2 (width) × 2 (depth) × 3 (height) = 12 cubes

✔ Volume: 12 cubes

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6)

Looks like a 3×3×2 block, but missing one cube?

Wait — it’s 3 cubes high, 2 cubes wide, 3 cubes deep?

Wait — let’s see:

- Height: 3 levels
- Width: 2 cubes
- Depth: 3 cubes?

But the drawing shows a U-shape or something?

No — it's a solid block?

Wait — no, it's missing one cube.

Look: it's a 3×2×3 block? No.

Actually, it's:
- 3 cubes high
- 2 cubes wide
- 3 cubes deep

But is it solid?

No — the top layer has a gap.

Wait — from the drawing:
- Bottom layer: 6 cubes (2×3)
- Middle layer: 6 cubes
- Top layer: 5 cubes? No — it’s missing one?

Wait — actually, the top layer has a gap.

Wait — no, it looks like:
- Each layer is 2×3 = 6 cubes
- But the top layer has a hole?

No — the drawing shows a solid block.

Wait — no, it’s a 3×2×3 block? Let’s count:

- Depth: 3 units (front to back)
- Width: 2 units (left to right)
- Height: 3 units

So total: 3 × 2 × 3 = 18 cubes?

But wait — it doesn’t look like that.

Actually, it’s a rectangular prism: 3 cubes tall, 2 cubes wide, 3 cubes deep.

So: 3 × 2 × 3 = 18 cubes

But wait — is it solid?

Yes — from the drawing, it appears to be a solid block.

Wait — no! Look again.

The top layer has only 5 cubes? No — it’s drawn as a solid block.

Actually, it's 3×2×3 = 18? That seems too big.

Wait — let’s recheck.

Perhaps it’s 3 cubes high, 3 cubes wide, 2 cubes deep?

No — it’s wider than deep.

Wait — the shape has:
- 3 levels
- At each level: 2 columns of 3 cubes?

Wait — no.

Better: count per layer.

Layer 1 (bottom): 6 cubes (3 across, 2 deep)
Layer 2 (middle): 6 cubes
Layer 3 (top): 6 cubes

So 6 × 3 = 18 cubes

But wait — the drawing shows only 6 cubes per layer? Yes.

But let’s verify with dimensions.

It’s a 3×3×2 block? No.

Wait — actually, it's 3 cubes high, 3 cubes wide, and 2 cubes deep?

But the drawing shows 3 cubes wide (left to right), 2 cubes deep (front to back), 3 cubes high.

So: 3 × 2 × 3 = 18 cubes.

But let’s confirm.

Yes — it's a solid rectangular prism: 3×2×3 = 18 cubes

✔ Volume: 18 cubes

Wait — but that seems large. Let me double-check.

Wait — no! Actually, it’s 3 cubes high, 2 cubes wide, 3 cubes deep — so yes, 3×2×3=18.

But maybe it’s not solid?

Wait — looking at the drawing, it appears solid.

Yes — all positions filled.

So ✔ Volume: 18 cubes

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7)

A 2×2×2 block with an extra cube attached?

Wait — it’s a 2×3×2 block?

Wait — let’s count:

- Bottom layer: 4 cubes (2×2)
- Top layer: 4 cubes (2×2)
- But one cube missing?

No — it’s a 2×2×2 cube with a 2×1×1 extension?

Wait — no.

Actually, it’s a 3×2×2 block?

Wait — it has:
- 3 cubes in width
- 2 cubes in depth
- 2 cubes in height

So: 3 × 2 × 2 = 12 cubes?

But let’s count.

Bottom layer:
- 3 cubes in a row (front)
- 3 cubes in a row (back)? No — only 2 deep.

Wait — the shape is:
- 3 cubes long (left to right)
- 2 cubes deep (front to back)
- 2 cubes high

So: 3 × 2 × 2 = 12 cubes

But is it solid?

Yes — appears to be a solid rectangular prism.

So ✔ Volume: 12 cubes

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8)

A 3×2×2 block? Or 2×2×3?

Wait — it’s a 3×2×2 block?

Wait — it’s 3 cubes high, 2 cubes wide, 2 cubes deep?

No — it’s 3 cubes high, 2 cubes wide, 2 cubes deep?

But the drawing shows:

- 3 levels
- Each level: 2×2 = 4 cubes
- So 3 × 4 = 12 cubes

Yes — it’s a solid block: 3×2×2 = 12 cubes

✔ Volume: 12 cubes

Wait — same as #7? Possibly.

But #7 was also 12.

Yes.

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9)

A flat shape: 2 cubes high, 3 cubes long, 1 cube deep?

Wait — it’s a 2×3×1 block?

Wait — it’s 2 cubes high, 3 cubes long, 1 cube deep.

But is it solid?

Yes — it’s a single layer of 3 cubes, stacked in 2 levels.

Wait — no — it’s 2 cubes high, 3 cubes long, 1 cube deep.

So: 2 × 3 × 1 = 6 cubes

But wait — it looks like a 3×2 rectangle, stacked?

No — it’s a 3-cube-long bar, with 2 cubes high.

So: 3 cubes in length, 1 in depth, 2 in height → 3×1×2 = 6 cubes

✔ Volume: 6 cubes

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Now let’s compile all answers.

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Final Answers:

1) 5 cubes
2) 4 cubes
3) 8 cubes
4) 4 cubes
5) 12 cubes
6) 18 cubes
7) 12 cubes
8) 12 cubes
9) 6 cubes

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Let me double-check each one.

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Rechecking:

1)
- Bottom: 3 cubes (L-shape)
- Middle: 1 cube
- Top: 1 cube
→ 5 ✔

2)
- 4 cubes stacked → 4 ✔

3)
- 2×2×2 = 8 ✔

4)
- Looks like a 2×2 base with one cube missing? No — it's a 2×2×2 with one missing? Wait — no.

Wait — I think I made a mistake here.

Let’s re-examine #4.

4)

Drawing: two cubes stacked on the left, and one cube in front of each.

Actually, it’s:
- Left column: 2 cubes high
- Right column: 1 cube high
- But both have a front cube?

Wait — it’s a 2×2×2 block missing the top-right cube?

No — it’s a T-shaped or L-shaped?

Wait — it’s:
- Bottom layer: 3 cubes (left-front, left-back, right-back)
- Top layer: 1 cube (on top of left-back)

So total: 4 cubes ✔

Yes.

5)
2×2×3 = 12 ✔

6)
3×2×3 = 18 ✔

7)
3×2×2 = 12 ✔

8)
2×2×3 = 12 ✔

9)
3×2×1 = 6 ✔

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✔ Final Answer:

| Shape | Volume |
|-------|--------|
| 1) | 5 cubes |
| 2) | 4 cubes |
| 3) | 8 cubes |
| 4) | 4 cubes |
| 5) | 12 cubes |
| 6) | 18 cubes |
| 7) | 12 cubes |
| 8) | 12 cubes |
| 9) | 6 cubes |

You can now fill in the blanks accordingly.