Volume cubes worksheet for calculating the volume of 3D shapes using unit cubes.

To find the volume of each shape, we count the number of unit cubes in each figure. Each cube represents 1 cubic centimeter ($cm^3$).

Here is the step-by-step count for each shape:

a.
* Bottom layer: 4 cubes long $\times$ 2 cubes wide = 8 cubes.
* Top layer: 4 cubes long $\times$ 1 cube wide = 4 cubes.
* Total: $8 + 4 = 12$

b.
* Let's count by columns or layers.
* Bottom layer: There is a row of 3 and two sticking out front. That's 5 cubes.
* Middle layer: Sits on top of the back row. That's 3 cubes.
* Top layer: Sits on the leftmost cube of the middle layer. That's 1 cube.
* Wait, let's look closer. It looks like an L-shape standing up.
* Left column stack: 3 high.
* Middle column stack: 2 high.
* Right column stack: 1 high.
* Front row: 1 cube in front of the left stack? No, looking at perspective, it looks like a corner piece.
* Let's try counting visible faces and inferring hidden ones.
* Back row (left to right): Stack of 3, Stack of 2, Stack of 1. ($3+2+1=6$)
* Front row: There is 1 cube in front of the bottom of the left stack.
* Total: $6 + 1 = 7$.

c.
* This is a flat rectangular prism.
* Length: 5 cubes.
* Width: 2 cubes.
* Height: 1 cube.
* Total: $5 \times 2 \times 1 = 10$.

d.
* This is a rectangular block with a chunk missing or just irregular. Let's count stacks.
* Left column: 4 high.
* Middle column: 3 high.
* Right column: 2 high.
* Depth: It looks 1 cube deep everywhere.
* Total: $4 + 3 + 2 = 9$.

e.
* This is a large rectangular block with a hole.
* Outer dimensions: 4 wide, 3 high, 2 deep. Total if solid = $4 \times 3 \times 2 = 24$.
* The hole is in the middle. It looks like it goes all the way through the depth (2 cubes deep). The hole is 2 cubes wide and 1 cube high? Or is the bottom missing?
* Let's count directly instead.
* Left slice (2 wide, 3 high, 2 deep): $2 \times 3 \times 2 = 12$ cubes.
* Right slice (2 wide, 3 high, 2 deep): $2 \times 3 \times 2 = 12$ cubes.
* Wait, the gap is in the middle. The structure is 4 units wide. The gap is 2 units wide. So there are two pillars on the sides? No, looking at the top, it's a U-shape or bridge.
* Let's count the bottom layer: 4 wide $\times$ 2 deep = 8 cubes.
* Middle layer: Two ends are filled. Left end (1 wide $\times$ 2 deep) + Right end (1 wide $\times$ 2 deep) = 4 cubes. The middle 2 spaces are empty.
* Top layer: Same as middle. Left end + Right end = 4 cubes.
* Total: $8 (\text{bottom}) + 4 (\text{middle}) + 4 (\text{top}) = 16$.

f.
* This is a U-shape.
* Left tower: 1 wide, 2 deep, 3 high = $1 \times 2 \times 3 = 6$ cubes.
* Right tower: 1 wide, 2 deep, 3 high = $1 \times 2 \times 3 = 6$ cubes.
* Bridge connecting them: 2 wide, 2 deep, 1 high? No, looking at the top, the bridge connects the tops? No, the bridge is at the bottom?
* Let's re-examine. It looks like two towers of height 3 connected by a lower section.
* Actually, usually these are uniform depth. Let's assume depth is 1 for simplicity unless shown otherwise. In 'f', the side view shows depth. The front face has width. The top shows depth.
* Left part: 1 wide, 3 high. Depth appears to be 2 (based on the top surface showing 2 squares deep). So $1 \times 3 \times 2 = 6$.
* Right part: 1 wide, 3 high. Depth 2. So $1 \times 3 \times 2 = 6$.
* Middle part: Connects them at the bottom? The drawing shows a connection at the bottom level. The gap is 2 cubes wide. The connection is 1 cube high. Depth is 2. So $2 \times 1 \times 2 = 4$.
* Total: $6 + 6 + 4 = 16$.

g.
* Pyramid style stack.
* Bottom layer: 3 wide $\times$ 2 deep? Let's trace the footprint.
* Back row: 3 cubes.
* Front row: 2 cubes (centered?).
* Let's count stacks.
* Back-left: 1 high. Back-middle: 2 high. Back-right: 1 high.
* Front-middle: 1 high?
* Let's look at the highest point. It's 2 high.
* Center stack is 2 high.
* Surrounding it: Left, Right, Back, Front.
* It looks like a cross shape on the bottom with one on top.
* Bottom layer: 5 cubes (center + 4 arms).
* Top layer: 1 cube (on center).
* Total: $5 + 1 = 6$.

h.
* Staircase shape.
* Left stack: 3 high.
* Middle stack: 2 high.
* Right stack: 1 high.
* Depth: Looks like 1 cube deep.
* Total: $3 + 2 + 1 = 6$.

i.
* Square block with a hole?
* Outer dimensions: 3 wide, 3 high, 1 deep? Or 2 deep?
* Looking at the top, it shows a 3x2 grid? No, it looks like a 3x3 square face, but perspective suggests depth.
* Let's assume depth is 1 first. If depth is 1:
* Total spots in 3x3 grid = 9.
* Missing center? The drawing shows lines inside. It looks like a frame.
* Top row: 3 cubes.
* Middle row: Left 1, Right 1. Center is empty.
* Bottom row: 3 cubes.
* Total: $3 + 2 + 3 = 8$.
* Does it have depth? The top surface shows 3 squares going back? No, just one row of tops. So depth is likely 1.
* Answer: 8.

j.
* Irregular stack.
* Left stack: 2 high.
* Middle stack: 3 high.
* Right stack: 1 high.
* Front: There is one cube in front of the middle stack?
* Let's trace carefully.
* Back row: Left (2 high), Middle (3 high), Right (1 high). Sum = $2+3+1=6$.
* Front row: One cube in front of the bottom of the middle stack. Sum = 1.
* Total: $6 + 1 = 7$.

k.
* Rectangular prism with a bite taken out?
* It looks like two blocks joined.
* Left block: 2 wide, 2 high, 2 deep?
* Right block: 2 wide, 2 high, 2 deep?
* Let's count by vertical slices.
* Left slice (2 wide): Height 2, Depth 2. Volume = $2 \times 2 \times 2 = 8$.
* Right slice (2 wide): Height 2, Depth 2. Volume = $2 \times 2 \times 2 = 8$.
* Are they connected? Yes. Is it a single 4x2x2 block?
* $4 \times 2 \times 2 = 16$.
* Let's verify the lines. The top shows 4 squares across, 2 deep. The front shows 4 across, 2 high. The side shows 2 deep, 2 high.
* It is a solid rectangular prism.
* Total: $4 \times 2 \times 2 = 16$.

l.
* Zig-zag or stairs turning a corner?
* Let's count stacks.
* Back-left stack: 2 high.
* Front-left stack: 1 high.
* Front-right stack: 2 high?
* Let's trace the connections.
* There is a column of 2 in the back left.
* Attached to its front is a column of 1.
* Attached to the right of that front column is another column of 1?
* And attached to the right of *that* is a column of 2?
* Let's look at the top surfaces.
* Top of back-left stack (height 2).
* Top of front-left stack (height 1).
* Top of front-right stack (height 1).
* Top of far-right stack (height 2).
* This interpretation seems complex. Let's try simpler.
* Maybe it's a 2x2 base?
* Back-Left: 2 high.
* Front-Left: 1 high.
* Back-Right: Empty?
* Front-Right: 2 high?
* Let's look at the image 'l' again.
* It looks like an 'L' shape of columns.
* Column 1 (Back Left): 2 cubes high.
* Column 2 (Front Left): 1 cube high.
* Column 3 (Front Right): 2 cubes high.
* Are there any others? It looks like just these three columns clustered.
* Total: $2 + 1 + 2 = 5$.

Let's double check l.
Looking at the perspective, the "Front Right" column might actually be "Back Right" if the "Front Left" is in front of "Back Left".
Usually, these grids align.
Let's assume a 2x2 grid footprint.
- Back-Left: Height 2.
- Front-Left: Height 1.
- Front-Right: Height 2.
- Back-Right: Height 0 (empty).
Total: $2 + 1 + 2 = 5$.

Let's double check b.
- Left stack: 3 high.
- Middle stack: 2 high.
- Right stack: 1 high.
- Front: 1 cube in front of the Left stack.
Total: $3 + 2 + 1 + 1 = 7$. Correct.

Let's double check f.
- Left Tower: 1x2 base, 3 high = 6.
- Right Tower: 1x2 base, 3 high = 6.
- Connector: Spans the gap between them. Gap is 2 units wide. Height is 1 unit. Depth is 2 units.
- Connector volume: $2 \times 1 \times 2 = 4$.
- Total: $6 + 6 + 4 = 16$. Correct.

Let's double check e.
- Bottom layer: Full 4x2 rectangle = 8.
- Middle layer: Ends only. Left 1x2, Right 1x2. Total 4.
- Top layer: Ends only. Left 1x2, Right 1x2. Total 4.
- Total: $8 + 4 + 4 = 16$. Correct.

Let's double check g.
- Center stack: 2 high.
- Four surrounding stacks (N, S, E, W): 1 high each.
- Total: $2 + 1 + 1 + 1 + 1 = 6$. Correct.

Final List:
a. 12
b. 7
c. 10
d. 9
e. 16
f. 16
g. 6
h. 6
i. 8
j. 7
k. 16
l. 5

Final Answer:
a. 12 cm³
b. 7 cm³
c. 10 cm³
d. 9 cm³
e. 16 cm³
f. 16 cm³
g. 6 cm³
h. 6 cm³
i. 8 cm³
j. 7 cm³
k. 16 cm³
l. 5 cm³