Volume of a cylinder worksheet - Free Printable
Educational worksheet: Volume of a cylinder worksheet. Download and print for classroom or home learning activities.
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Step-by-step solution for: Volume of a cylinder worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Volume of a cylinder worksheet
Let’s solve each cylinder volume problem step by step.
The formula for the volume of a cylinder is:
Volume = π × r² × h
Where:
- r = radius (half of the diameter)
- h = height
- π ≈ 3.14159 (we’ll use this value and round final answers to nearest hundredth)
---
- Diameter = 8 cm → Radius = 8 ÷ 2 = 4 cm
- Height = 12 cm
Volume = π × 4² × 12
= 3.14159 × 16 × 12
= 3.14159 × 192
≈ 603.19 cm³
*(Note: The worksheet says “cm²” but that’s a typo — volume should be in cubic units, cm³. We’ll write the number as requested.)*
---
- Diameter = 5 m → Radius = 5 ÷ 2 = 2.5 m
- Height = 3 m
Volume = π × (2.5)² × 3
= 3.14159 × 6.25 × 3
= 3.14159 × 18.75
≈ 58.90 m³
---
- Radius = 31 mm (already given as radius, not diameter!)
- Height = 77 mm
Volume = π × 31² × 77
= 3.14159 × 961 × 77
First: 961 × 77 = 73,997
Then: 3.14159 × 73,997 ≈ 232,474.77 mm³
Wait — let me double-check that multiplication:
31² = 961 ✔️
961 × 77:
Break it down:
961 × 70 = 67,270
961 × 7 = 6,727
Total = 67,270 + 6,727 = 73,997 ✔️
Now: 3.14159 × 73,997
Let’s compute:
3 × 73,997 = 221,991
0.14159 × 73,997 ≈ ?
0.1 × 73,997 = 7,399.7
0.04 × 73,997 = 2,959.88
0.00159 × 73,997 ≈ 117.655
Add them: 7,399.7 + 2,959.88 = 10,359.58 + 117.655 ≈ 10,477.235
Total volume ≈ 221,991 + 10,477.235 = 232,468.235
Rounded to nearest hundredth: 232,468.24 mm³
*(Earlier I had 232,474.77 — that was a small error. Corrected now.)*
Actually, let me use calculator-style precision:
π × 961 × 77 = π × 73997 ≈ 3.1415926535 × 73997 ≈ 232,468.24
Yes, correct.
---
- Diameter = 14 cm → Radius = 14 ÷ 2 = 7 cm
- Height = 9 cm
Volume = π × 7² × 9
= 3.14159 × 49 × 9
= 3.14159 × 441
≈ 1,385.44 cm³
Check: 49 × 9 = 441 ✔️
3.14159 × 441:
3 × 441 = 1,323
0.14159 × 441 ≈ 62.44119
Total ≈ 1,323 + 62.44119 = 1,385.44119 → rounds to 1,385.44
---
- Radius = 2 cm (given as radius)
- Height = 6 cm
Volume = π × 2² × 6
= 3.14159 × 4 × 6
= 3.14159 × 24
≈ 75.40 cm³
Check: 4 × 6 = 24
3.14159 × 24 = 75.39816 → rounds to 75.40
---
- Diameter = 9 m → Radius = 9 ÷ 2 = 4.5 m
- Height = 6 m
Volume = π × (4.5)² × 6
= 3.14159 × 20.25 × 6
First: 20.25 × 6 = 121.5
Then: 3.14159 × 121.5 ≈ ?
3 × 121.5 = 364.5
0.14159 × 121.5 ≈ 17.203185
Total ≈ 364.5 + 17.203185 = 381.703185 → rounds to 381.70 m³
Double-check with direct calc:
π × 20.25 × 6 = π × 121.5 ≈ 3.1415926535 × 121.5 ≈ 381.7035 → still 381.70
---
## Final Answers (rounded to nearest hundredth):
Top Left: 603.19
Top Right: 58.90
Middle Left: 232468.24
Middle Right: 1385.44
Bottom Left: 75.40
Bottom Right: 381.70
*(Note: All volumes are technically in cubic units — cm³ or m³ — even though the worksheet writes cm² or m². We’re filling in the numbers as requested.)*
Final Answer:
603.19, 58.90, 232468.24, 1385.44, 75.40, 381.70
The formula for the volume of a cylinder is:
Volume = π × r² × h
Where:
- r = radius (half of the diameter)
- h = height
- π ≈ 3.14159 (we’ll use this value and round final answers to nearest hundredth)
---
Cylinder 1: Top Left
- Diameter = 8 cm → Radius = 8 ÷ 2 = 4 cm
- Height = 12 cm
Volume = π × 4² × 12
= 3.14159 × 16 × 12
= 3.14159 × 192
≈ 603.19 cm³
*(Note: The worksheet says “cm²” but that’s a typo — volume should be in cubic units, cm³. We’ll write the number as requested.)*
---
Cylinder 2: Top Right
- Diameter = 5 m → Radius = 5 ÷ 2 = 2.5 m
- Height = 3 m
Volume = π × (2.5)² × 3
= 3.14159 × 6.25 × 3
= 3.14159 × 18.75
≈ 58.90 m³
---
Cylinder 3: Middle Left
- Radius = 31 mm (already given as radius, not diameter!)
- Height = 77 mm
Volume = π × 31² × 77
= 3.14159 × 961 × 77
First: 961 × 77 = 73,997
Then: 3.14159 × 73,997 ≈ 232,474.77 mm³
Wait — let me double-check that multiplication:
31² = 961 ✔️
961 × 77:
Break it down:
961 × 70 = 67,270
961 × 7 = 6,727
Total = 67,270 + 6,727 = 73,997 ✔️
Now: 3.14159 × 73,997
Let’s compute:
3 × 73,997 = 221,991
0.14159 × 73,997 ≈ ?
0.1 × 73,997 = 7,399.7
0.04 × 73,997 = 2,959.88
0.00159 × 73,997 ≈ 117.655
Add them: 7,399.7 + 2,959.88 = 10,359.58 + 117.655 ≈ 10,477.235
Total volume ≈ 221,991 + 10,477.235 = 232,468.235
Rounded to nearest hundredth: 232,468.24 mm³
*(Earlier I had 232,474.77 — that was a small error. Corrected now.)*
Actually, let me use calculator-style precision:
π × 961 × 77 = π × 73997 ≈ 3.1415926535 × 73997 ≈ 232,468.24
Yes, correct.
---
Cylinder 4: Middle Right
- Diameter = 14 cm → Radius = 14 ÷ 2 = 7 cm
- Height = 9 cm
Volume = π × 7² × 9
= 3.14159 × 49 × 9
= 3.14159 × 441
≈ 1,385.44 cm³
Check: 49 × 9 = 441 ✔️
3.14159 × 441:
3 × 441 = 1,323
0.14159 × 441 ≈ 62.44119
Total ≈ 1,323 + 62.44119 = 1,385.44119 → rounds to 1,385.44
---
Cylinder 5: Bottom Left
- Radius = 2 cm (given as radius)
- Height = 6 cm
Volume = π × 2² × 6
= 3.14159 × 4 × 6
= 3.14159 × 24
≈ 75.40 cm³
Check: 4 × 6 = 24
3.14159 × 24 = 75.39816 → rounds to 75.40
---
Cylinder 6: Bottom Right
- Diameter = 9 m → Radius = 9 ÷ 2 = 4.5 m
- Height = 6 m
Volume = π × (4.5)² × 6
= 3.14159 × 20.25 × 6
First: 20.25 × 6 = 121.5
Then: 3.14159 × 121.5 ≈ ?
3 × 121.5 = 364.5
0.14159 × 121.5 ≈ 17.203185
Total ≈ 364.5 + 17.203185 = 381.703185 → rounds to 381.70 m³
Double-check with direct calc:
π × 20.25 × 6 = π × 121.5 ≈ 3.1415926535 × 121.5 ≈ 381.7035 → still 381.70
---
## Final Answers (rounded to nearest hundredth):
Top Left: 603.19
Top Right: 58.90
Middle Left: 232468.24
Middle Right: 1385.44
Bottom Left: 75.40
Bottom Right: 381.70
*(Note: All volumes are technically in cubic units — cm³ or m³ — even though the worksheet writes cm² or m². We’re filling in the numbers as requested.)*
Final Answer:
603.19, 58.90, 232468.24, 1385.44, 75.40, 381.70
Parent Tip: Review the logic above to help your child master the concept of volume cylinder worksheet.
