Let’s solve each problem one by one. We’re finding volumes of cylinders and spheres, rounding to the nearest tenth.
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Problem 1: Cylinder
Given:
- Radius = 3 ft
- Height = 4 ft
Formula for volume of a cylinder:
V = π × r² × h
Plug in numbers:
V = π × (3)² × 4
V = π × 9 × 4
V = π × 36
V ≈ 3.1416 × 36 ≈
113.1 ft³
✔ Final Answer for #1:
113.1 ft³
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Problem 2: Sphere
Given:
- Diameter = 8 cm → so radius = 4 cm
Formula for volume of a sphere:
V = (4/3) × π × r³
Plug in numbers:
V = (4/3) × π × (4)³
V = (4/3) × π × 64
V = (256/3) × π
V ≈ 85.333 × 3.1416 ≈
268.1 cm³
✔ Final Answer for #2:
268.1 cm³
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Problem 3: Sphere
Given:
- Radius = 7 yd
V = (4/3) × π × r³
V = (4/3) × π × 343
V = (1372/3) × π
V ≈ 457.333 × 3.1416 ≈
1436.8 yd³
✔ Final Answer for #3:
1436.8 yd³
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Problem 4: Sphere
Given:
- Diameter = 10 m → radius = 5 m
V = (4/3) × π × (5)³
V = (4/3) × π × 125
V = (500/3) × π
V ≈ 166.667 × 3.1416 ≈
523.6 m³
✔ Final Answer for #4:
523.6 m³
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Problem 5: Sphere
Given:
- Radius = 11 mm
V = (4/3) × π × (11)³
V = (4/3) × π × 1331
V = (5324/3) × π
V ≈ 1774.667 × 3.1416 ≈
5575.3 mm³
✔ Final Answer for #5:
5575.3 mm³
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Problem 6: Cylinder
Given:
- Radius = 10 in
- Height = 12 in
V = π × r² × h
V = π × 100 × 12
V = π × 1200
V ≈ 3.1416 × 1200 ≈
3769.9 in³
✔ Final Answer for #6:
3769.9 in³
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Problem 7: Cylinder
Given:
- Radius = 4 ft
- Height = 9 ft
V = π × (4)² × 9
V = π × 16 × 9
V = π × 144
V ≈ 3.1416 × 144 ≈
452.4 ft³
✔ Final Answer for #7:
452.4 ft³
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Problem 8: Cylinder
Given:
- Radius = 6 cm
- Height = 15 cm
V = π × (6)² × 15
V = π × 36 × 15
V = π × 540
V ≈ 3.1416 × 540 ≈
1696.5 cm³
✔ Final Answer for #8:
1696.5 cm³
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Problem 9: Cylinder
Given:
- Radius = 2 m
- Height = 10 m
V = π × (2)² × 10
V = π × 4 × 10
V = π × 40
V ≈ 3.1416 × 40 ≈
125.7 m³
✔ Final Answer for #9:
125.7 m³
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Problem 10: Cylinder
Given:
- Radius = 5 in
- Height = 8 in
V = π × (5)² × 8
V = π × 25 × 8
V = π × 200
V ≈ 3.1416 × 200 ≈
628.3 in³
✔ Final Answer for #10:
628.3 in³
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Final Answer:
1. 113.1 ft³
2. 268.1 cm³
3. 1436.8 yd³
4. 523.6 m³
5. 5575.3 mm³
6. 3769.9 in³
7. 452.4 ft³
8. 1696.5 cm³
9. 125.7 m³
10. 628.3 in³
Parent Tip: Review the logic above to help your child master the concept of worksheet volume of cones cylinder and spheres answers.
