Let’s solve each problem step by step.
We are counting unit cubes to find the volume of each rectangular prism.
Each cube = 1 ft³, so we just count how many cubes fit inside each shape.
To do this easily, we can multiply:
Length × Width × Height (in cubes) → that gives us the total number of cubes → which equals the volume in ft³.
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Problem 1:
Looks like a tall block. Let’s count:
- Front face: 4 cubes wide, 6 cubes high → but wait, let’s check depth too.
Actually, looking at it:
It’s 3 cubes deep (front to back), 4 cubes wide (left to right), and 6 cubes tall (top to bottom).
So: 3 × 4 × 6 = 72
✔ Volume =
72 ft³
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Problem 2:
This one is flat and wide.
Count:
- Length (left to right): 6 cubes
- Width (front to back): 4 cubes
- Height (top to bottom): 3 cubes
So: 6 × 4 × 3 = 72
✔ Volume =
72 ft³
Wait — let me double-check. Maybe I miscounted height?
Looking again: yes, 3 layers high. 6 long, 4 wide → 6×4=24 per layer × 3 layers = 72. Correct.
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Problem 3:
Smaller block.
Count:
- Width: 3 cubes
- Depth: 3 cubes
- Height: 5 cubes
So: 3 × 3 × 5 = 45
✔ Volume =
45 ft³
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Problem 4:
Small rectangle.
Count:
- Length: 4 cubes
- Width: 3 cubes
- Height: 2 cubes
So: 4 × 3 × 2 = 24
✔ Volume =
24 ft³
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Problem 5:
Flat and long.
Count:
- Length: 6 cubes
- Width: 4 cubes
- Height: 1 cube (only one layer!)
So: 6 × 4 × 1 = 24
✔ Volume =
24 ft³
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Problem 6:
Big cube-like shape.
Count:
- Each side looks like 6 cubes.
Check: length = 6, width = 6, height = 6? Wait — no, actually, looking closely:
It’s 6 wide, 6 deep, and 6 high? That would be 216 — but let’s verify.
Actually, from the drawing:
Front face shows 6 across and 6 up. And since it’s a cube, depth is also 6.
Yes: 6 × 6 × 6 = 216
✔ Volume =
216 ft³
Wait — hold on! Is it really 6x6x6? Let me look again.
Actually, in the image, for #6, it appears to be 6 units wide, 6 units deep, and 6 units high — yes, it’s a perfect cube made of smaller cubes. So 6³ = 216. Correct.
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Problem 7:
Long low block.
Count:
- Length: 6 cubes
- Width: 3 cubes
- Height: 2 cubes
So: 6 × 3 × 2 = 36
✔ Volume =
36 ft³
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Problem 8:
Tall thin tower.
Count:
- Width: 2 cubes
- Depth: 2 cubes
- Height: 8 cubes
So: 2 × 2 × 8 = 32
✔ Volume =
32 ft³
Wait — let me check height. From top to bottom, how many cubes?
Yes, 8 cubes tall. Base is 2x2. So 4 per layer × 8 layers = 32. Correct.
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Problem 9:
Another block.
Count:
- Width: 4 cubes
- Depth: 3 cubes
- Height: 6 cubes
So: 4 × 3 × 6 = 72
✔ Volume =
72 ft³
Wait — let me confirm dimensions.
Front view: 4 wide, 6 high. Side view suggests 3 deep. Yes. 4×3×6=72. Correct.
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Now let’s list all answers clearly:
1) 72
2) 72
3) 45
4) 24
5) 24
6) 216
7) 36
8) 32
9) 72
I’ll go through once more to make sure I didn’t mix any up.
#1: 3×4×6=72 ✔️
#2: 6×4×3=72 ✔️
#3: 3×3×5=45 ✔️
#4: 4×3×2=24 ✔️
#5: 6×4×1=24 ✔️
#6: 6×6×6=216 ✔️
#7: 6×3×2=36 ✔️
#8: 2×2×8=32 ✔️
#9: 4×3×6=72 ✔️
All correct!
Final Answer:
1) 72
2) 72
3) 45
4) 24
5) 24
6) 216
7) 36
8) 32
9) 72
Parent Tip: Review the logic above to help your child master the concept of volume rectangular prism worksheet answers.
