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MathsAges 13-15

Volume of cylinders & cones

Calculate the volume of a right circular cylinder (V = πr²h) or cone (V = ⅓πr²h) using π = 3.14. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Volume of cylinders & cones

Take your time. Show your thinking.

  1. 1. A right circular cylinder has base radius 7 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 7 cm, h = 30 cm · V = πr²h

  2. 2. A right circular cylinder has base radius 5 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 5 cm, h = 3 cm · V = πr²h

  3. 3. A right circular cylinder has base radius 5 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 5 cm, h = 21 cm · V = πr²h

  4. 4. A right circular cone has base radius 3 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    Cone: r = 3 cm, h = 21 cm · V = ⅓πr²h

  5. 5. A right circular cylinder has base radius 8 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 8 cm, h = 27 cm · V = πr²h

  6. 6. A right circular cone has base radius 3 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.

    Cone: r = 3 cm, h = 9 cm · V = ⅓πr²h

  7. 7. A right circular cone has base radius 3 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.

    Cone: r = 3 cm, h = 15 cm · V = ⅓πr²h

  8. 8. A right circular cylinder has base radius 9 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 9 cm, h = 6 cm · V = πr²h

  9. 9. A right circular cone has base radius 10 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    Cone: r = 10 cm, h = 6 cm · V = ⅓πr²h

  10. 10. A right circular cone has base radius 10 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    Cone: r = 10 cm, h = 30 cm · V = ⅓πr²h

  11. 11. A right circular cone has base radius 2 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.

    Cone: r = 2 cm, h = 18 cm · V = ⅓πr²h

  12. 12. A right circular cone has base radius 7 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    Cone: r = 7 cm, h = 6 cm · V = ⅓πr²h
12 questions · Seed 42 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Volume of cylinders & cones

Answers and reasoning. Review before teaching.

  1. 1. A right circular cylinder has base radius 7 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    4615.8 cm³

    Volume V = πr²h = 3.14 × 7² × 30 = 4615.8 cm³.

  2. 2. A right circular cylinder has base radius 5 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.

    235.5 cm³

    Volume V = πr²h = 3.14 × 5² × 3 = 235.5 cm³.

  3. 3. A right circular cylinder has base radius 5 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    1648.5 cm³

    Volume V = πr²h = 3.14 × 5² × 21 = 1648.5 cm³.

  4. 4. A right circular cone has base radius 3 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    197.82 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 3² × 21 = 197.82 cm³.

  5. 5. A right circular cylinder has base radius 8 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.

    5425.92 cm³

    Volume V = πr²h = 3.14 × 8² × 27 = 5425.92 cm³.

  6. 6. A right circular cone has base radius 3 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.

    84.78 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 3² × 9 = 84.78 cm³.

  7. 7. A right circular cone has base radius 3 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.

    141.3 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 3² × 15 = 141.3 cm³.

  8. 8. A right circular cylinder has base radius 9 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    1526.04 cm³

    Volume V = πr²h = 3.14 × 9² × 6 = 1526.04 cm³.

  9. 9. A right circular cone has base radius 10 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    628 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 10² × 6 = 628 cm³.

  10. 10. A right circular cone has base radius 10 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    3140 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 10² × 30 = 3140 cm³.

  11. 11. A right circular cone has base radius 2 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.

    75.36 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 2² × 18 = 75.36 cm³.

  12. 12. A right circular cone has base radius 7 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    307.72 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 7² × 6 = 307.72 cm³.

12 questions · Seed 42 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Volume of cylinders & cones

Take your time. Show your thinking.

  1. 1. A right circular cylinder has base radius 7 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 7 cm, h = 30 cm · V = πr²h

  2. 2. A right circular cylinder has base radius 5 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 5 cm, h = 3 cm · V = πr²h

  3. 3. A right circular cylinder has base radius 5 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 5 cm, h = 21 cm · V = πr²h

  4. 4. A right circular cone has base radius 3 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    Cone: r = 3 cm, h = 21 cm · V = ⅓πr²h

  5. 5. A right circular cylinder has base radius 8 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 8 cm, h = 27 cm · V = πr²h

  6. 6. A right circular cone has base radius 3 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.

    Cone: r = 3 cm, h = 9 cm · V = ⅓πr²h

  7. 7. A right circular cone has base radius 3 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.

    Cone: r = 3 cm, h = 15 cm · V = ⅓πr²h

  8. 8. A right circular cylinder has base radius 9 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    Cylinder: r = 9 cm, h = 6 cm · V = πr²h

  9. 9. A right circular cone has base radius 10 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    Cone: r = 10 cm, h = 6 cm · V = ⅓πr²h

  10. 10. A right circular cone has base radius 10 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    Cone: r = 10 cm, h = 30 cm · V = ⅓πr²h

  11. 11. A right circular cone has base radius 2 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.

    Cone: r = 2 cm, h = 18 cm · V = ⅓πr²h

  12. 12. A right circular cone has base radius 7 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    Cone: r = 7 cm, h = 6 cm · V = ⅓πr²h
12 questions · Seed 42 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Volume of cylinders & cones

Answers and reasoning. Review before teaching.

  1. 1. A right circular cylinder has base radius 7 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    4615.8 cm³

    Volume V = πr²h = 3.14 × 7² × 30 = 4615.8 cm³.

  2. 2. A right circular cylinder has base radius 5 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.

    235.5 cm³

    Volume V = πr²h = 3.14 × 5² × 3 = 235.5 cm³.

  3. 3. A right circular cylinder has base radius 5 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    1648.5 cm³

    Volume V = πr²h = 3.14 × 5² × 21 = 1648.5 cm³.

  4. 4. A right circular cone has base radius 3 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.

    197.82 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 3² × 21 = 197.82 cm³.

  5. 5. A right circular cylinder has base radius 8 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.

    5425.92 cm³

    Volume V = πr²h = 3.14 × 8² × 27 = 5425.92 cm³.

  6. 6. A right circular cone has base radius 3 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.

    84.78 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 3² × 9 = 84.78 cm³.

  7. 7. A right circular cone has base radius 3 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.

    141.3 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 3² × 15 = 141.3 cm³.

  8. 8. A right circular cylinder has base radius 9 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    1526.04 cm³

    Volume V = πr²h = 3.14 × 9² × 6 = 1526.04 cm³.

  9. 9. A right circular cone has base radius 10 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    628 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 10² × 6 = 628 cm³.

  10. 10. A right circular cone has base radius 10 cm and perpendicular height 30 cm. Using π = 3.14, calculate its volume.

    3140 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 10² × 30 = 3140 cm³.

  11. 11. A right circular cone has base radius 2 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.

    75.36 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 2² × 18 = 75.36 cm³.

  12. 12. A right circular cone has base radius 7 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.

    307.72 cm³

    Volume V = ⅓πr²h = ⅓ × 3.14 × 7² × 6 = 307.72 cm³.

12 questions · Seed 42 · Age guidance, not curriculum certification