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

Let’s go shape by shape and count the cubes carefully.

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Shape 1)
We see a base of 3 cubes in a row, and on the rightmost cube, there are 2 more stacked on top.
So: 3 (bottom) + 2 (on top of one) = 5 cubes

Wait — let me double-check:
Actually, looking again: It’s like an L-shape with height.
Bottom layer: 3 cubes in a straight line? No — actually, it looks like 2 cubes side-by-side at front, and behind them is a column of 3 cubes high.
Better way: Count visible and hidden.

Actually, standard interpretation for these diagrams:

Shape 1:
- Front-left: 1 cube
- Behind that: a stack of 3 cubes (so 3 total in that column)
- To the right of the front-left: 1 cube (same level as bottom)
But wait — if you look closely, it's probably:

It’s a 2x2 base but missing one corner, and one tower of 3.

Alternative approach: Let’s imagine layers.

Layer 1 (bottom):
There are 4 cubes? Wait no.

Actually, from common worksheet patterns:

Shape 1:
Think of it as:
- A column of 3 cubes (vertical)
- Attached to its left at the bottom: 2 cubes going sideways (like an L on the ground)

So: 3 (tower) + 2 (base extension) = 5? But the two base extensions might be sharing space?

No — better to count each cube individually.

Visual breakdown:

Imagine coordinates:

Set origin at bottom-front-left.

Cube at (0,0,0) — bottom front left
Cube at (1,0,0) — bottom front right
Cube at (0,1,0) — bottom back left
Then above (0,1,0): (0,1,1) and (0,1,2) → so 2 more on top of back-left

Total: positions:
(0,0,0), (1,0,0), (0,1,0), (0,1,1), (0,1,2) → that’s 5 cubes.

✔ Shape 1: 5

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Shape 2)
Just a straight vertical tower of 5 cubes. Easy.

✔ Shape 2: 5

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Shape 3)
Looks like a 2x2 square base, and 2 layers high.

So: 2 × 2 × 2 = 8 cubes.

Check: Bottom layer: 4 cubes. Top layer: 4 cubes directly above. Total 8.

✔ Shape 3: 8

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Shape 4)
This one is tricky. Looks like a 2x2 base, but only 3 cubes on bottom? And then some on top.

Breakdown:

Bottom layer:
Front row: 2 cubes
Back row: only 1 cube (left side) — so 3 cubes on bottom.

Top layer:
On top of the back-left cube: 1 cube
On top of the front-left cube: 1 cube
Front-right has nothing on top.

So top layer: 2 cubes.

Total: 3 (bottom) + 2 (top) = 5

Wait — let me visualize again.

Actually, standard view:

It’s like a staircase or corner.

Another way:
Left column: 2 cubes high (front and back both have 2?) No.

Perhaps:

Positions:

(0,0,0), (1,0,0) — front row bottom
(0,1,0) — back left bottom
Above (0,0,0): (0,0,1)
Above (0,1,0): (0,1,1)

That’s 5 cubes:
(0,0,0), (1,0,0), (0,1,0), (0,0,1), (0,1,1)

Yes — 5 cubes.

✔ Shape 4: 5

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Shape 5)
A rectangular prism: 2 cubes wide, 1 deep, 5 high? Or 2x1x5?

Looking: It’s 2 columns side by side, each 5 cubes tall.

So: 2 × 5 = 10 cubes.

✔ Shape 5: 10

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Shape 6)
Looks like 2 columns side by side, each 4 cubes tall? But also connected in front?

Wait — actually, it’s a 2x2 base, 4 layers high? No.

From diagram: It appears to be 2 cubes wide, 2 cubes deep? No — depth seems 1.

Actually, looking: It’s 2 columns (side by side), each 4 cubes high, and they’re connected at every level? So still just 2×4=8? But that doesn’t match the drawing.

Wait — perhaps it’s 2 wide, 1 deep, 4 high → 8 cubes? But the drawing shows something thicker.

Alternative: Maybe it’s 2x2 base, 4 high? That would be 16 — too big.

Look again: The shape has a “notch” on top? No — actually, it’s solid.

Standard interpretation: This is a 2x2x4 block? But drawn in perspective.

Counting layers:

Each horizontal slice (layer) has 4 cubes? Because it’s 2 wide and 2 deep? In the drawing, you can see front face has 2 columns, and side face shows depth of 2.

Yes — so it’s 2 (width) × 2 (depth) × 4 (height) = 16? But that seems too large for this worksheet.

Wait — look at shape 8 — which is similar but smaller.

Actually, comparing to shape 3 (which was 2x2x2=8), shape 6 looks taller.

In shape 6: You can count the vertical lines — there are 4 levels.

And in each level, how many cubes? From the front, you see 2 cubes per row, and since it goes back 2 rows (you can see the side), so 2x2=4 per layer.

4 layers × 4 = 16.

But let me verify with another method.

List all positions:

Assume x (left-right), y (front-back), z (up-down)

For z=0 to 3 (4 levels)

At each z, cubes at:

(x=0,y=0), (x=1,y=0), (x=0,y=1), (x=1,y=1) → 4 per layer

Total: 4 × 4 = 16

But is that correct? Looking at the drawing — yes, it’s a full 2x2x4 block.

However, in some worksheets, sometimes they draw it differently.

Wait — compare to shape 8: shape 8 is 2x2x3 = 12? We’ll get to that.

But for now, I think shape 6 is 16.

But let me check online or standard answers — no, I must reason.

Another thought: In shape 6, the top layer might be missing some? No, it looks solid.

Perhaps it’s only 2 wide and 1 deep? Then 2×4=8.

But the drawing clearly shows depth — you can see the side faces.

In fact, in the diagram, for shape 6, you can see three faces: front, top, and side — indicating it’s 3D with depth.

Specifically, the top view would show 2x2 grid.

So yes, 2x2x4 = 16.

But let’s hold on — maybe I’m overcomplicating.

Let me count visibly and infer hidden.

Front face: 2 columns × 4 high = 8 cubes visible on front.

But behind each of those, there is another cube (since depth is 2), so another 8 behind? No — that would be double-counting.

Better: Each "column" in the front corresponds to a stack that goes back 2 cubes.

So for each of the 2 front positions, there are 2 cubes deep, and 4 high → 2 × 2 × 4 = 16.

Yes.

✔ Shape 6: 16

Wait — but let's cross-validate with other shapes.

Shape 8 is similar but shorter — we'll do that next.

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Shape 7)
This looks like a 3x2 base but with some missing.

Base layer: Let's say 3 cubes in front row, 2 in back row? Or vice versa.

From drawing: It seems like a 2x3 rectangle but with one corner cut out? No.

Actually, it's like a U-shape or something.

Count:

Bottom layer:
Front: 3 cubes
Back: only 2 cubes (missing the middle or end?)

Looking: Probably, it's 2 rows deep.

Row 1 (front): 3 cubes
Row 2 (back): 2 cubes (say, left and right, missing middle) — but that doesn't make sense.

Standard way: Imagine from top.

Top view: It's almost a 2x3 grid, but missing one cube.

Specifically, likely: positions where cubes exist:

(0,0,0), (1,0,0), (2,0,0) — front row
(0,1,0), (2,1,0) — back row, missing (1,1,0)
Then on top of some:
Above (0,0,0): (0,0,1)
Above (0,1,0): (0,1,1)
Above (2,0,0): ? Not sure.

Actually, from the drawing, it seems:

The left part has 2 layers: front-left and back-left both have 2 cubes high.

The middle front has 1 cube (only bottom).

The right part: front-right has 1 cube, back-right has 1 cube — both only bottom.

So let's list:

- (0,0,0), (0,0,1) — left front, 2 high
- (0,1,0), (0,1,1) — left back, 2 high
- (1,0,0) — middle front, 1 high
- (2,0,0) — right front, 1 high
- (2,1,0) — right back, 1 high

Is that all? What about (1,1,0)? Probably not present.

So cubes:
(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (2,0,0), (2,1,0) → that's 7 cubes.

Count: 7.

✔ Shape 7: 7

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Shape 8)
Similar to shape 6 but shorter.

If shape 6 was 2x2x4=16, then shape 8 should be 2x2x3=12.

Confirm: 3 layers, each with 4 cubes (2x2).

Yes.

✔ Shape 8: 12

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Shape 9)
Flat shape — only 1 layer high.

Looks like a 3x2 grid? 3 long, 2 wide.

So 3 × 2 = 6 cubes.

From drawing: front row 3 cubes, back row 3 cubes — yes, 6.

✔ Shape 9: 6

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Now, let's summarize all:

1) 5
2) 5
3) 8
4) 5
5) 10
6) 16
7) 7
8) 12
9) 6

But wait — I recall that in some versions of this worksheet, shape 6 might be different. Let me double-check shape 6.

Upon second thought, in shape 6, is it really 2x2x4?

Looking at the drawing: The height is 4, width is 2, but depth — when you look at the side, you see 2 cubes deep? Yes.

But let's count the number of cube faces visible.

Alternatively, think of it as: each "stack" is 4 high, and there are 4 stacks (2x2), so 16.

But perhaps in this context, it's intended to be simpler.

Compare to shape 5: which is 2x1x5=10 — that makes sense.

Shape 6: if it were 2x2x4, it's 16, which is fine.

But let me see if there's a mistake.

Another idea: in shape 6, the top layer might be only 2 cubes? No, the drawing shows a full top layer.

Perhaps it's 2 wide, 2 deep, 4 high — yes.

I think 16 is correct.

But to be thorough, let's consider if any cubes are hidden or not.

No, it's a solid block.

So I'll stick with 16.

Final list:

1: 5
2: 5
3: 8
4: 5
5: 10
6: 16
7: 7
8: 12
9: 6

Now, write the answer as per format.

Since ExplainAnswer is false, TeachTopic is false, GeneratePractice is false, I only provide Final Answer.

But the instruction says: "Complete ALL reasoning and explanations BEFORE writing the Final Answer." and then "Final Answer: [Provide only the final correct answer]"

And since all options are false, I omit those sections, but I did the reasoning above.

So for Final Answer, I need to present the answers for all 9 shapes.

Probably as a list or in order.

The worksheet has blanks for each, so I should provide the numbers in order.

Final Answer:
1) 5
2) 5
3) 8
4) 5
5) 10
6) 16
7) 7
8) 12
9) 6

To make it clear, perhaps comma-separated or something.

But the instruction says "provide only the final correct answer", and since it's multiple parts, I should list them.

I think listing as above is fine.

Some might expect a single string, but I think structured is better.

Since it's a worksheet, the answer is the volumes for each.

So:

Final Answer:
5, 5, 8, 5, 10, 16, 7, 12, 6

Or with labels.

But to match the format, perhaps just the numbers in order.

I think it's safe to write:

Final Answer:
1) 5
2) 5
3) 8
4) 5
5) 10
6) 16
7) 7
8) 12
9) 6

Yes.