Measures and solids · Ages 14–15

Volume of a cone worksheet

Part of: Cones & spheres

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Measures and solids · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The cone in the picture has a base radius of 9 cm and a height of 19 cm. What is its volume, in terms of π?
Answer:
2.Taking π as 3.14, what is the volume of the cone in the picture (radius 5 cm, height 3 cm), in cm³?
Answer:
3.Taking π as 3.14, what is the volume of the cone in the picture (radius 4 cm, height 9 cm), in cm³?
Answer:
4.The cone in the picture has a base radius of 7 cm and a height of 12 cm. What is its volume, in terms of π?
Answer:
5.The cone in the picture has a base radius of 4 cm and a volume of 16π cm³. How high is it, in cm?
Answer:
6.The cone in the picture has a base radius of 15 cm and a slant height of 39 cm. What is its volume, in terms of π?
Answer:
7.The cone in the picture has a base radius of 12 cm and a volume of 816π cm³. How high is it, in cm?
Answer:
8.The cone in the picture has a base radius of 14 cm and a height of 19 cm. Correct to 1 decimal place, what is its volume, in cm³?
Answer:
9.The cone in the picture is 9 cm high and has a volume of 75π cm³. What is its base radius, in cm?
Answer:

10.The cone in the picture is 6 cm across its base and 12 cm high. What is its volume?
- A. 36π cm³
- B. 144π cm³
- C. 12π cm³
- D. 108π cm³
Choose the right answer
Answer:
11.The cone in the picture is 4 cm across its base and 15 cm high. What is its volume?
- A. 20π cm³
- B. 60π cm³
- C. 80π cm³
- D. 10π cm³
Choose the right answer
Answer:
12.A cone of base radius 7 cm and height 21 cm has a volume of 1029π cm³.
True or false?
Answer:

13.A cone-shaped paper cup is 4 cm in radius at the top and holds 280 mL. Correct to 1 decimal place, how deep is it, in cm?
Working:
Answer:
14.A pile of sand is a cone 8 m across its base and 4 m high. Correct to 1 decimal place, what is its volume, in m³?
Working:
Answer:
15.A cone-shaped ice cream cone is 3 cm in radius at its mouth and 12 cm deep. It holds π cm³ in terms of π, and cm³ taking π as 3.14.
Fill in each blank
Working:
Answer:
16.A cone-shaped funnel is 42 cm in radius at its mouth, its slanting side 58 cm long. The funnel is cm deep and holds π cm³ when full.
Fill in each blank
Working:
Answer:
17.A cone-shaped paper cup is 4 cm in radius at the top and holds 330 mL. Correct to 1 decimal place, how deep is it, in cm?
Working:
Answer:
18.A pile of sand is a cone 15 m across its base and 6 m high. Correct to 1 decimal place, what is its volume, in m³?
Working:
Answer:

Show the answers and working

Volume of a cone worksheet: Answers and working

1. 513 π cm³
13 × π × 9² × 19 = 13 × 81π × 19 = 513π cm³.
2. 78.5 cm³
13 × π × 5² × 3 = 25π; with 3.14, 78.5 cm³.
3. 150.72 cm³
13 × π × 4² × 9 = 48π; with 3.14, 150.72 cm³.
4. 196 π cm³
13 × π × 7² × 12 = 13 × 49π × 12 = 196π cm³.
5. 3 cm
13 × 16π × h = 16π, so h = 3 × 16 ÷ 16 = 3 cm.
6. 2700 π cm³
The height by Pythagoras' theorem first: 39² − 15² = 36 cm; volume 13 × π × 15² × 36 = 2700π cm³.
7. 17 cm
13 × 144π × h = 816π, so h = 3 × 816 ÷ 144 = 17 cm.
8. 3899.8 cm³
13 × π × 14² × 19 with the calculator's π, rounded at the end: about 3899.8 cm³.
9. 5 cm
13 × πr² × 9 = 75π, so r² = 3 × 75 ÷ 9 = 25 and r = 5 cm.

10. A. 36π cm³
Radius 3: 13 × π × 3² × 12 = 36π cm³.
11. A. 20π cm³
Radius 2: 13 × π × 2² × 15 = 20π cm³.
12. False
13 × π × 7² × 21 = 343π cm³: a cone is a third of the cylinder on its base.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 16.7 cm
1 mL = 1 cm³: 13 × π × 4² × h = 280, so h = 3 × 280 ÷ (π × 4²) ≈ 16.7 cm.
14. 67 m³
Radius 8 ÷ 2; 13 × π × radius² × 4, rounded at the end: about 67 m³.
15. 36, 113.04
13 × π × 3² × 12 = 36π; × 3.14 = 113.04.
16. 40, 23520
58² − 42² = 40; 13 × π × 42² × 40 = 23520π.
17. 19.7 cm
1 mL = 1 cm³: 13 × π × 4² × h = 330, so h = 3 × 330 ÷ (π × 4²) ≈ 19.7 cm.
18. 353.4 m³
Radius 15 ÷ 2; 13 × π × radius² × 6, rounded at the end: about 353.4 m³.

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