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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Worksheet StudioPractice pack · Ages 13-15

Volume of cylinders & cones

Take your time. Show your thinking.

1. A right circular cylinder has base radius 7 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 7 cm, h = 18 cm · V = πr²h
2. A right circular cylinder has base radius 6 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 6 cm, h = 12 cm · V = πr²h
3. A right circular cone has base radius 12 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
Cone: r = 12 cm, h = 12 cm · V = ⅓πr²h
4. A right circular cylinder has base radius 11 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 11 cm, h = 21 cm · V = πr²h
5. A right circular cone has base radius 11 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
Cone: r = 11 cm, h = 12 cm · V = ⅓πr²h
6. A right circular cone has base radius 4 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
Cone: r = 4 cm, h = 3 cm · V = ⅓πr²h
7. A right circular cone has base radius 8 cm and perpendicular height 24 cm. Using π = 3.14, calculate its volume.
Cone: r = 8 cm, h = 24 cm · V = ⅓πr²h
8. A right circular cylinder has base radius 5 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 5 cm, h = 15 cm · V = πr²h
9. A right circular cone has base radius 12 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.
Cone: r = 12 cm, h = 27 cm · V = ⅓πr²h
10. A right circular cone has base radius 4 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.
Cone: r = 4 cm, h = 6 cm · V = ⅓πr²h
11. A right circular cone has base radius 7 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
Cone: r = 7 cm, h = 3 cm · V = ⅓πr²h
12. A right circular cylinder has base radius 2 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 2 cm, h = 9 cm · V = πr²h

12 questions · Seed 44 · 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. A right circular cylinder has base radius 7 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.
2769.48 cm³
Volume V = πr²h = 3.14 × 7² × 18 = 2769.48 cm³.
2. A right circular cylinder has base radius 6 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
1356.48 cm³
Volume V = πr²h = 3.14 × 6² × 12 = 1356.48 cm³.
3. A right circular cone has base radius 12 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
1808.64 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 12² × 12 = 1808.64 cm³.
4. A right circular cylinder has base radius 11 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.
7978.74 cm³
Volume V = πr²h = 3.14 × 11² × 21 = 7978.74 cm³.
5. A right circular cone has base radius 11 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
1519.76 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 11² × 12 = 1519.76 cm³.
6. A right circular cone has base radius 4 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
50.24 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 4² × 3 = 50.24 cm³.
7. A right circular cone has base radius 8 cm and perpendicular height 24 cm. Using π = 3.14, calculate its volume.
1607.68 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 8² × 24 = 1607.68 cm³.
8. A right circular cylinder has base radius 5 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.
1177.5 cm³
Volume V = πr²h = 3.14 × 5² × 15 = 1177.5 cm³.
9. A right circular cone has base radius 12 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.
4069.44 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 12² × 27 = 4069.44 cm³.
10. A right circular cone has base radius 4 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.
100.48 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 4² × 6 = 100.48 cm³.
11. A right circular cone has base radius 7 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
153.86 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 7² × 3 = 153.86 cm³.
12. A right circular cylinder has base radius 2 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.
113.04 cm³
Volume V = πr²h = 3.14 × 2² × 9 = 113.04 cm³.

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Volume of cylinders & cones

Take your time. Show your thinking.

1. A right circular cylinder has base radius 7 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 7 cm, h = 18 cm · V = πr²h
2. A right circular cylinder has base radius 6 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 6 cm, h = 12 cm · V = πr²h
3. A right circular cone has base radius 12 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
Cone: r = 12 cm, h = 12 cm · V = ⅓πr²h
4. A right circular cylinder has base radius 11 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 11 cm, h = 21 cm · V = πr²h
5. A right circular cone has base radius 11 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
Cone: r = 11 cm, h = 12 cm · V = ⅓πr²h
6. A right circular cone has base radius 4 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
Cone: r = 4 cm, h = 3 cm · V = ⅓πr²h
7. A right circular cone has base radius 8 cm and perpendicular height 24 cm. Using π = 3.14, calculate its volume.
Cone: r = 8 cm, h = 24 cm · V = ⅓πr²h
8. A right circular cylinder has base radius 5 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 5 cm, h = 15 cm · V = πr²h
9. A right circular cone has base radius 12 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.
Cone: r = 12 cm, h = 27 cm · V = ⅓πr²h
10. A right circular cone has base radius 4 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.
Cone: r = 4 cm, h = 6 cm · V = ⅓πr²h
11. A right circular cone has base radius 7 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
Cone: r = 7 cm, h = 3 cm · V = ⅓πr²h
12. A right circular cylinder has base radius 2 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.
Cylinder: r = 2 cm, h = 9 cm · V = πr²h

12 questions · Seed 44 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Volume of cylinders & cones

Answers and reasoning. Review before teaching.

1. A right circular cylinder has base radius 7 cm and perpendicular height 18 cm. Using π = 3.14, calculate its volume.
2769.48 cm³
Volume V = πr²h = 3.14 × 7² × 18 = 2769.48 cm³.
2. A right circular cylinder has base radius 6 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
1356.48 cm³
Volume V = πr²h = 3.14 × 6² × 12 = 1356.48 cm³.
3. A right circular cone has base radius 12 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
1808.64 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 12² × 12 = 1808.64 cm³.
4. A right circular cylinder has base radius 11 cm and perpendicular height 21 cm. Using π = 3.14, calculate its volume.
7978.74 cm³
Volume V = πr²h = 3.14 × 11² × 21 = 7978.74 cm³.
5. A right circular cone has base radius 11 cm and perpendicular height 12 cm. Using π = 3.14, calculate its volume.
1519.76 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 11² × 12 = 1519.76 cm³.
6. A right circular cone has base radius 4 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
50.24 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 4² × 3 = 50.24 cm³.
7. A right circular cone has base radius 8 cm and perpendicular height 24 cm. Using π = 3.14, calculate its volume.
1607.68 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 8² × 24 = 1607.68 cm³.
8. A right circular cylinder has base radius 5 cm and perpendicular height 15 cm. Using π = 3.14, calculate its volume.
1177.5 cm³
Volume V = πr²h = 3.14 × 5² × 15 = 1177.5 cm³.
9. A right circular cone has base radius 12 cm and perpendicular height 27 cm. Using π = 3.14, calculate its volume.
4069.44 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 12² × 27 = 4069.44 cm³.
10. A right circular cone has base radius 4 cm and perpendicular height 6 cm. Using π = 3.14, calculate its volume.
100.48 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 4² × 6 = 100.48 cm³.
11. A right circular cone has base radius 7 cm and perpendicular height 3 cm. Using π = 3.14, calculate its volume.
153.86 cm³
Volume V = ⅓πr²h = ⅓ × 3.14 × 7² × 3 = 153.86 cm³.
12. A right circular cylinder has base radius 2 cm and perpendicular height 9 cm. Using π = 3.14, calculate its volume.
113.04 cm³
Volume V = πr²h = 3.14 × 2² × 9 = 113.04 cm³.

12 questions · Seed 44 · Age guidance, not curriculum certification