Math worksheet for calculating volume by counting unit cubes in various 3D shapes.

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

We’ll look at how many cubes are in each layer, then multiply by the number of layers (or just count row by row if it’s easier).

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1)
This is a rectangular block.
Front view: 3 cubes wide × 2 cubes high = 6 cubes per layer.
Depth: 2 layers deep.
So total = 6 × 2 = 12 cubes

Wait — let me double-check by counting rows:

Top layer: 3 across × 2 deep = 6
Bottom layer: same = 6
Total = 6 + 6 = 12

✔ Correct.

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2)
This one is taller.
Width: 2 cubes
Height: 4 cubes
Depth: 2 cubes? Wait — looking again...

Actually, from the drawing:
It’s 2 cubes wide (left to right),
4 cubes tall (top to bottom),
and 2 cubes deep (front to back)? No — wait, let’s count visible faces.

Better way: Count front face first.

Front face has 2 columns × 4 rows = 8 cubes.
But since it’s 2 cubes deep? Actually, no — looking at the perspective, this shape is only 1 cube deep? Wait — no, that can’t be.

Wait — actually, in these drawings, when you see lines going “back”, that means depth.

In problem 2:
You can see 2 cubes across (width),
4 cubes up (height),
and 2 cubes going back (depth) — because there are two sets of vertical lines on the side.

So: width=2, height=4, depth=2 → 2×4×2 = 16

But let’s count manually:

Layer 1 (front): 2 wide × 4 high = 8
Layer 2 (back): same = 8
Total = 16

✔ Yes.

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3)
Looks like a cube made of smaller cubes.
Each side: 3 cubes long.
So 3 × 3 × 3 = 27

Count:
Top layer: 3×3 = 9
Middle layer: 9
Bottom layer: 9
Total = 27

✔ Correct.

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4)
Tall thin tower.
Width: 2 cubes
Height: 5 cubes
Depth: 1 cube? Let’s check.

From the drawing: It’s 2 cubes wide (side by side),
5 cubes tall,
and only 1 cube deep (no lines going backward — it’s flat in depth).

So: 2 × 5 × 1 = 10

Count: Each column has 5 cubes, and there are 2 columns → 5+5=10

✔ Correct.

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5)
Big flat rectangle.
Width: 5 cubes
Height: 4 cubes
Depth: 1 cube? Again, no depth shown — looks like a single layer.

Wait — actually, looking at the lines: There are lines going back — so depth is 2?

Wait — let’s analyze:

Front face: 5 wide × 4 high = 20
But is it 1 or 2 deep?

Looking at the top edge — you can see two rows going back → so depth = 2.

So: 5 × 4 × 2 = 40

Count: Front layer: 5×4=20, Back layer: 20 → total 40

✔ Yes.

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6)
Another big cube-like shape.
Width: 4 cubes
Height: 3 cubes
Depth: 3 cubes? Let’s see.

From the drawing:
Front face: 4 wide × 3 high
And you can see 3 layers going back (because of the grid lines on top and side)

So: 4 × 3 × 3 = 36

Count:
Each horizontal layer (from front to back) has 4×3=12 cubes
There are 3 such layers → 12×3=36

✔ Correct.

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7)
Long flat shape.
Width: 5 cubes
Height: 2 cubes
Depth: 3 cubes? Let’s check.

Front face: 5 wide × 2 high = 10
How many layers deep? Looking at the top — you can see 3 rows going back → depth=3

So: 5 × 2 × 3 = 30

Count:
Each layer (front to back) has 5×2=10
Three layers → 10×3=30

✔ Correct.

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8)
Similar to #1 but bigger.
Width: 4 cubes
Height: 2 cubes
Depth: 2 cubes? Let’s see.

Front face: 4 wide × 2 high = 8
Depth: 2 layers (you can see two sets of lines going back)

So: 4 × 2 × 2 = 16

Count:
Front layer: 8 cubes
Back layer: 8 cubes
Total = 16

✔ Correct.

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Now let’s list all answers clearly:

1) 12
2) 16
3) 27
4) 10
5) 40
6) 36
7) 30
8) 16

Final Answer:
1) 12
2) 16
3) 27
4) 10
5) 40
6) 36
7) 30
8) 16