Students calculate the volume of each 3D shape by counting the number of unit cubes.
A worksheet titled "Finding the Volume by Counting Cubes" showing 10 3D shapes made of unit cubes, each labeled with a number, with a key indicating one cubic unit.
JPG
365×480
23.6 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #295962
⭐
Show Answer Key & Explanations
Step-by-step solution for: Measuring volume of odd shaped cubes worksheet
▼
Show Answer Key & Explanations
Step-by-step solution for: Measuring volume of odd shaped cubes worksheet
Let's solve the problem step by step.
The task is to find the volume of each 3D shape by counting the number of cubic units in each figure. Each small cube represents 1 cubic unit, so we just need to count how many cubes are in each shape.
We’ll go through each shape one by one:
---
This shape has:
- Bottom layer: 4 cubes (2×2)
- Middle layer: 3 cubes (top-left, center, and top-right — but only 3)
- Top layer: 2 cubes
Wait — let’s carefully analyze it.
Actually, looking at the structure:
- Front row: 3 cubes high on the left, 2 cubes high in middle, 1 cube high on right
- Back row: 2 cubes high on left, 1 cube high in middle, nothing on right?
Wait — better to count layers.
Let me reconstruct this properly.
It looks like:
- Layer 1 (bottom): 4 cubes (2×2 base)
- Layer 2: 3 cubes (on top of 3 of the bottom ones)
- Layer 3: 2 cubes (on top of 2 of the second layer)
But wait — actually, it's a stacked L-shape.
Looking closely:
- The base is 3 cubes wide and 2 deep? No.
Better to use layer-by-layer counting.
Let’s do it systematically.
---
Visual:
```
□□
□□
□□□
```
No — better to imagine it as:
- From front to back, left to right.
Actually, from the image:
- It has:
- 3 columns in the front row: heights 3, 2, 1
- 2 columns in the back row: heights 2, 1
So:
- Front row: 3 + 2 + 1 = 6
- Back row: 2 + 1 = 3
- Total = 6 + 3 = 9
✔ Answer: 9 cubic units
---
Looks like a pyramid-like structure.
Front row:
- Left: 3 cubes high
- Middle: 2 cubes high
- Right: 1 cube high
Back row:
- Left: 2 cubes high
- Middle: 1 cube high
- Right: 0
So:
- Front: 3 + 2 + 1 = 6
- Back: 2 + 1 = 3
- Total = 6 + 3 = 9
✔ Answer: 9 cubic units
---
Small shape:
- Base: 2×2 = 4 cubes?
- But only 3 cubes shown?
Wait: it’s:
- Bottom layer: 3 cubes (in an L-shape)
- Top layer: 1 cube on top of the corner
So:
- Bottom: 3 cubes
- Top: 1 cube
- Total = 4
✔ Answer: 4 cubic units
---
Tall rectangular prism.
Looks like:
- 3 layers high
- 3 cubes wide
- 2 cubes deep
So: 3 × 3 × 2 = 18
Or count:
- Each layer: 3×2 = 6 cubes
- 3 layers → 6 × 3 = 18
✔ Answer: 18 cubic units
---
Looks like a stepped rectangle.
From front to back:
- Front row: 3 cubes long, height 2
- Back row: 2 cubes long, height 2
Wait — no:
Actually:
- Two rows: front and back
- Front row: 3 cubes wide, 2 high → 3×2 = 6
- Back row: 2 cubes wide, 2 high → 2×2 = 4
- But are they stacked?
Wait — no, it's more like:
- Bottom layer: 5 cubes (3 in front, 2 behind)
- Top layer: 3 cubes (only over front 3)
So:
- Bottom: 5
- Top: 3
- Total = 8
Yes, that matches.
✔ Answer: 8 cubic units
---
Looks like:
- Base: 3×3 = 9 cubes
- On top: 2 cubes added (on the right side)
Wait — let’s see:
- Bottom layer: 3×3 = 9
- Second layer: 2 cubes (on the right side, on top of two bottom cubes)
- Third layer: 1 cube on top of that
Wait — no, it’s not stacked fully.
Actually:
- Bottom: 3×3 = 9
- Middle: 2 cubes (on top of the rightmost column)
- Top: 1 cube (on top of those)
But wait — the structure shows:
- A full 3×3 base
- Then on the right side, a stack of 2 more cubes on top of the back-right and middle-right
- And then one more on top of that?
Wait — no, it's simpler:
Looking at it:
- The shape has:
- A 3×3 base (9 cubes)
- On the right side, a tower of 2 cubes (on the back-right and middle-right)
- But no third layer?
Wait — actually, it's:
- Bottom: 3×3 = 9
- Middle: 2 cubes (on top of the back-right and middle-right)
- Top: 1 cube (on top of the middle-right)
So:
- Bottom: 9
- Middle: 2
- Top: 1
- Total = 9 + 2 + 1 = 12
✔ Answer: 12 cubic units
---
Very small:
- Base: 2 cubes (side by side)
- On top: 1 cube (on the left one)
- On top of that: 1 more cube
So:
- Bottom: 2
- Middle: 1
- Top: 1
- Total = 2 + 1 + 1 = 4
✔ Answer: 4 cubic units
---
Looks like:
- Base: 3 cubes in a line
- On top: 1 cube on the middle
- On top of that: 1 cube
Wait — or:
- Bottom: 3 cubes
- Middle: 1 cube (on the middle)
- Top: 1 cube (on top of that)
So:
- 3 + 1 + 1 = 5
✔ Answer: 5 cubic units
---
Large rectangular block.
Looks like:
- 3 layers high
- 4 cubes wide
- 3 cubes deep
Wait — check:
- Width: 4
- Depth: 3
- Height: 3
So: 4 × 3 × 3 = 36
Count:
- Each layer: 4×3 = 12
- 3 layers: 12 × 3 = 36
✔ Answer: 36 cubic units
---
Tall structure:
- Base: 3×3 = 9 cubes
- On top: 1 cube in the center
- On top of that: 1 more cube
So:
- Bottom: 9
- Middle: 1
- Top: 1
- Total = 9 + 1 + 1 = 11
✔ Answer: 11 cubic units
---
| Shape | Volume (cubic units) |
|-------|------------------------|
| 1 | 9 |
| 2 | 9 |
| 3 | 4 |
| 4 | 18 |
| 5 | 8 |
| 6 | 12 |
| 7 | 4 |
| 8 | 5 |
| 9 | 36 |
| 10 | 11 |
---
To find the volume of each shape:
1. Recognize that each small cube = 1 cubic unit.
2. Count all visible cubes, including hidden ones (e.g., under others).
3. Use layer-by-layer method: count each horizontal layer and sum.
4. Be careful with overlapping or stacked structures.
For complex shapes, break them into parts or use a grid-based approach.
Let me know if you'd like a visual breakdown for any specific shape!
The task is to find the volume of each 3D shape by counting the number of cubic units in each figure. Each small cube represents 1 cubic unit, so we just need to count how many cubes are in each shape.
We’ll go through each shape one by one:
---
1.
This shape has:
- Bottom layer: 4 cubes (2×2)
- Middle layer: 3 cubes (top-left, center, and top-right — but only 3)
- Top layer: 2 cubes
Wait — let’s carefully analyze it.
Actually, looking at the structure:
- Front row: 3 cubes high on the left, 2 cubes high in middle, 1 cube high on right
- Back row: 2 cubes high on left, 1 cube high in middle, nothing on right?
Wait — better to count layers.
Let me reconstruct this properly.
It looks like:
- Layer 1 (bottom): 4 cubes (2×2 base)
- Layer 2: 3 cubes (on top of 3 of the bottom ones)
- Layer 3: 2 cubes (on top of 2 of the second layer)
But wait — actually, it's a stacked L-shape.
Looking closely:
- The base is 3 cubes wide and 2 deep? No.
Better to use layer-by-layer counting.
Let’s do it systematically.
---
Shape 1
Visual:
```
□□
□□
□□□
```
No — better to imagine it as:
- From front to back, left to right.
Actually, from the image:
- It has:
- 3 columns in the front row: heights 3, 2, 1
- 2 columns in the back row: heights 2, 1
So:
- Front row: 3 + 2 + 1 = 6
- Back row: 2 + 1 = 3
- Total = 6 + 3 = 9
✔ Answer: 9 cubic units
---
Shape 2
Looks like a pyramid-like structure.
Front row:
- Left: 3 cubes high
- Middle: 2 cubes high
- Right: 1 cube high
Back row:
- Left: 2 cubes high
- Middle: 1 cube high
- Right: 0
So:
- Front: 3 + 2 + 1 = 6
- Back: 2 + 1 = 3
- Total = 6 + 3 = 9
✔ Answer: 9 cubic units
---
Shape 3
Small shape:
- Base: 2×2 = 4 cubes?
- But only 3 cubes shown?
Wait: it’s:
- Bottom layer: 3 cubes (in an L-shape)
- Top layer: 1 cube on top of the corner
So:
- Bottom: 3 cubes
- Top: 1 cube
- Total = 4
✔ Answer: 4 cubic units
---
Shape 4
Tall rectangular prism.
Looks like:
- 3 layers high
- 3 cubes wide
- 2 cubes deep
So: 3 × 3 × 2 = 18
Or count:
- Each layer: 3×2 = 6 cubes
- 3 layers → 6 × 3 = 18
✔ Answer: 18 cubic units
---
Shape 5
Looks like a stepped rectangle.
From front to back:
- Front row: 3 cubes long, height 2
- Back row: 2 cubes long, height 2
Wait — no:
Actually:
- Two rows: front and back
- Front row: 3 cubes wide, 2 high → 3×2 = 6
- Back row: 2 cubes wide, 2 high → 2×2 = 4
- But are they stacked?
Wait — no, it's more like:
- Bottom layer: 5 cubes (3 in front, 2 behind)
- Top layer: 3 cubes (only over front 3)
So:
- Bottom: 5
- Top: 3
- Total = 8
Yes, that matches.
✔ Answer: 8 cubic units
---
Shape 6
Looks like:
- Base: 3×3 = 9 cubes
- On top: 2 cubes added (on the right side)
Wait — let’s see:
- Bottom layer: 3×3 = 9
- Second layer: 2 cubes (on the right side, on top of two bottom cubes)
- Third layer: 1 cube on top of that
Wait — no, it’s not stacked fully.
Actually:
- Bottom: 3×3 = 9
- Middle: 2 cubes (on top of the rightmost column)
- Top: 1 cube (on top of those)
But wait — the structure shows:
- A full 3×3 base
- Then on the right side, a stack of 2 more cubes on top of the back-right and middle-right
- And then one more on top of that?
Wait — no, it's simpler:
Looking at it:
- The shape has:
- A 3×3 base (9 cubes)
- On the right side, a tower of 2 cubes (on the back-right and middle-right)
- But no third layer?
Wait — actually, it's:
- Bottom: 3×3 = 9
- Middle: 2 cubes (on top of the back-right and middle-right)
- Top: 1 cube (on top of the middle-right)
So:
- Bottom: 9
- Middle: 2
- Top: 1
- Total = 9 + 2 + 1 = 12
✔ Answer: 12 cubic units
---
Shape 7
Very small:
- Base: 2 cubes (side by side)
- On top: 1 cube (on the left one)
- On top of that: 1 more cube
So:
- Bottom: 2
- Middle: 1
- Top: 1
- Total = 2 + 1 + 1 = 4
✔ Answer: 4 cubic units
---
Shape 8
Looks like:
- Base: 3 cubes in a line
- On top: 1 cube on the middle
- On top of that: 1 cube
Wait — or:
- Bottom: 3 cubes
- Middle: 1 cube (on the middle)
- Top: 1 cube (on top of that)
So:
- 3 + 1 + 1 = 5
✔ Answer: 5 cubic units
---
Shape 9
Large rectangular block.
Looks like:
- 3 layers high
- 4 cubes wide
- 3 cubes deep
Wait — check:
- Width: 4
- Depth: 3
- Height: 3
So: 4 × 3 × 3 = 36
Count:
- Each layer: 4×3 = 12
- 3 layers: 12 × 3 = 36
✔ Answer: 36 cubic units
---
Shape 10
Tall structure:
- Base: 3×3 = 9 cubes
- On top: 1 cube in the center
- On top of that: 1 more cube
So:
- Bottom: 9
- Middle: 1
- Top: 1
- Total = 9 + 1 + 1 = 11
✔ Answer: 11 cubic units
---
✔ Final Answers:
| Shape | Volume (cubic units) |
|-------|------------------------|
| 1 | 9 |
| 2 | 9 |
| 3 | 4 |
| 4 | 18 |
| 5 | 8 |
| 6 | 12 |
| 7 | 4 |
| 8 | 5 |
| 9 | 36 |
| 10 | 11 |
---
🔍 Explanation Summary:
To find the volume of each shape:
1. Recognize that each small cube = 1 cubic unit.
2. Count all visible cubes, including hidden ones (e.g., under others).
3. Use layer-by-layer method: count each horizontal layer and sum.
4. Be careful with overlapping or stacked structures.
For complex shapes, break them into parts or use a grid-based approach.
Let me know if you'd like a visual breakdown for any specific shape!
Parent Tip: Review the logic above to help your child master the concept of volume of a cube worksheet.