Find the volume count the cubes worksheet - Free Printable

Explanation:
We are asked to find the volume of each shape by counting how many small cubes make up the shape. Each small cube counts as 1 unit of volume.

Let’s go one by one:

1) Shape 1:
Look at the layers.
- Bottom layer: 3 cubes in a row (left to right), and one cube behind the middle one → total 4 cubes on bottom.
- Middle layer: 2 cubes stacked on top of the rightmost two of the bottom layer.
- Top layer: 1 cube on top of the rightmost cube.
So: 4 (bottom) + 2 (middle) + 1 (top) = 7 cubes.

Wait — let me double-check carefully by counting visible cubes and hidden ones.

Better method: Count column by column (vertical stacks).

From left to right, front to back:

- Front-left column: 1 cube (only bottom).
- Front-middle column: 1 cube (bottom only) — but wait, there's a cube behind it? Let's sketch mentally.

Actually, standard way for these diagrams:
The shape looks like:
- A base of 3 cubes in a line (front row).
- Behind the middle cube of that line, there is another cube (so base has 4 cubes total).
- On top of the rightmost front cube: 2 more cubes stacked → so that column is height 3.
- On top of the middle front cube: 1 more cube → height 2.
- The left front cube: height 1.
- The back cube (behind middle front): height 1.

So columns:
- Front-left: 1
- Front-middle: 2
- Front-right: 3
- Back-middle: 1
Total = 1 + 2 + 3 + 1 = 7 ✔

2) Shape 2:
It’s a single vertical stack of 5 cubes.
So volume = 5.

3) Shape 3:
Looks like a 2×2×2 cube (2 cubes long, 2 wide, 2 high).
2 × 2 × 2 = 8 cubes.

4) Shape 4:
Let’s count columns:
- Front-left: 2 cubes (stacked)
- Front-right: 1 cube
- Back-left: 2 cubes (stacked behind front-left)
- Back-right: 1 cube (behind front-right)

Wait — better to visualize: It's like a 2×2 base (4 cubes), with 2 extra on top of the left two.

Base: 4 cubes (2x2 square).
On top of front-left and back-left: 1 cube each → +2
Total = 4 + 2 = 6

Yes — confirmed: 6 cubes.

5) Shape 5:
It’s a 2×1 base (2 cubes side by side), and 4 layers high.
So each column has 4 cubes, and there are 2 columns → 2 × 4 = 8.

6) Shape 6:
Looks like 2 columns side by side, each 4 cubes high → 2 × 4 = 8?
Wait — actually, from diagram: it's 2 cubes deep (front and back), and 2 wide, and 4 high? No.

Let me count:
The shape is rectangular: width = 2 cubes, depth = 2 cubes, height = 4 cubes?
But looking closely: the front face shows 2×4 = 8 cubes, and there’s a full back layer too? Actually, in isometric drawings, if you see a solid rectangle like that with no missing parts, and it looks like a full block, then yes — it’s 2 (wide) × 2 (deep) × 4 (high) = 16? That seems too big.

Wait — compare to shape 5: shape 5 is clearly 2×1×4 = 8.
Shape 6 is wider: it has 2 cubes side-by-side *and* appears to have depth of 2 (you can see both front and back rows). In the drawing, each layer has 4 cubes (2×2), and there are 4 layers → 4 × 4 = 16.

Yes — confirm: bottom layer: 2×2 = 4 cubes. 4 layers → 4×4 = 16.

7) Shape 7:
Looks like a 3×2×2 block? Let's count layers.

Front view: 3 cubes wide, 2 high. Depth = 2 (you see two rows). So volume = 3 × 2 × 2 = 12.

Check: bottom layer: 3×2 = 6 cubes. Top layer: same → 6. Total = 12. ✔

8) Shape 8:
Looks like 2×2×3: width 2, depth 2, height 3.
2 × 2 × 3 = 12.

Confirm: each layer is 2×2 = 4 cubes, and 3 layers → 4×3 = 12. ✔

9) Shape 9:
Looks like 3×2×1: width 3, depth 2, height 1 (flat).
3 × 2 × 1 = 6.

Double-check: you see 3 cubes in front row, 3 behind → 6 total. ✔

Now list all answers:

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

Let me verify #6 once more — because it's easy to miscount.

Shape 6: vertical tower, 4 high, and from front you see 2 cubes side-by-side, and you also see the back row (the lines show depth), so yes — it's 2 wide × 2 deep × 4 high = 16. Correct.

All others seem consistent.

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