Measures and solids · Ages 13–14

Volume of a cylinder worksheet

Part of: Cylinders

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Measures and solids · Ages 13–14

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

1.The cylinder in the picture has a base 4 cm across and a height of 8 cm. What is its volume, in terms of π?
Answer:
2.The cylinder in the picture has a base radius of 8 cm and a height of 18 cm. What is its volume, in terms of π?
Answer:
3.The cylinder in the picture has a base radius of 2 cm and a height of 6 cm. What is its volume, in terms of π?
Answer:
4.The cylinder in the picture has a volume of 40π cm³ and a base radius of 2 cm. How high is it, in cm?
Answer:
5.Using your calculator's π key, find the volume of the cylinder in the picture: radius 7 cm, height 20 cm. To 3 significant figures, what is it, in cm³?
Answer:
6.The cylinder in the picture has a volume of 18π cm³ and a base radius of 3 cm. How high is it, in cm?
Answer:
7.Using your calculator's π key, find the volume of the cylinder in the picture: radius 4 cm, height 15 cm. To 3 significant figures, what is it, in cm³?
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8.The cylinder in the picture has a volume of 16π cm³ and a height of 4 cm. What is its base radius r, in cm?
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9.Cylinder A's radius is 3 times cylinder B's, but A is only 12 as high as B. How many times B's volume is A's?
Answer in simplest form
Answer:
10.The cylinder in the picture has a volume of 160π cm³ and a height of 10 cm. What is its base radius r, in cm?
Answer:

11.The cylinder in the picture is 18 cm across and 15 cm high. What is its volume?
- A. 4860π cm³
- B. 270π cm³
- C. 1215π cm³
- D. 135π cm³
Choose the right answer
Answer:
12.A cylinder 16 cm across and 11 cm high has a volume of 176π cm³.
True or false?
Answer:

13.A cylindrical water tank on a roof has a base radius of 1 m and a height of 3 m. Using your calculator's π key, what is its capacity, in m³, to 3 significant figures?
Working:
Answer:
14.A can of soda is a cylinder of base radius 2 cm and height 13 cm. Its capacity in terms of π is π cm³; with your calculator's π key, to 3 significant figures, about mL.
Fill in each blank
Working:
Answer:
15.A cylindrical flowerpot holds 63π cm³ and is 7 cm high. Find its base radius: put the steps in order.
- A. πr² × 7 = 63π
- B. r = 9 = 3
- C. r² = 63 ÷ 7 = 9
Write the letters in the right order
Working:
Answer:
16.A metal rod, a cylinder of radius 2 cm and length 32 cm, is melted down and cast into round medals, cylinders of radius 1 cm and 0.25 cm thick, with nothing lost. How many medals can be made?
Working:
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17.A hose has an inner radius of 1 cm, and the water in it moves 100 cm every second. Using your calculator's π key, to 3 significant figures, how many litres flow out in 4 minutes?
Working:
Answer:
18.A round cake of radius 13 cm and height 4 cm is cut from the centre into 4 equal slices. What is each slice's volume, in terms of π?
Working:
Answer:

Show the answers and working

Volume of a cylinder worksheet: Answers and working

1. 32 π cm³
The radius is half the diameter, 4 ÷ 2 = 2 cm; volume π × 2² × 8 = 32π cm³.
2. 1152 π cm³
Base area π × 8² = 64π cm², volume = base area × height = 64π × 18 = 1152π cm³.
3. 24 π cm³
Base area π × 2² = 4π cm², volume = base area × height = 4π × 6 = 24π cm³.
4. 10 cm
The base area is π × 2² = 4π cm², so the height = volume ÷ base area = 40π ÷ 4π = 10 cm.
5. 3080 cm³
Work in π first: π × 7² × 20 = 980π, then press π at the end: 980π ≈ 3080 cm³ (3 significant figures).
6. 2 cm
The base area is π × 3² = 9π cm², so the height = volume ÷ base area = 18π ÷ 9π = 2 cm.
7. 754 cm³
Work in π first: π × 4² × 15 = 240π, then press π at the end: 240π ≈ 754 cm³ (3 significant figures).
8. 2 cm
πr² × 4 = 16π, so r² = 16 ÷ 4 = 4 and r = 2 cm (2 × 2 = 4).
9. 92 times
Volume πr²h: 3 times the radius makes r² 9 times; 12 the height, so 9 × 12 = 92 times the volume.
10. 4 cm
πr² × 10 = 160π, so r² = 160 ÷ 10 = 16 and r = 4 cm (4 × 4 = 16).

11. C. 1215π cm³
The radius is 18 ÷ 2 = 9 cm, so the volume is π × 9² × 15 = 1215π cm³.
12. False
The radius is 8 cm, so the volume is π × 8² × 11 = 704π cm³.

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

13. 9.42 m³
In π: π × 1² × 3 = 3π; press π at the end: 3π ≈ 9.42 m³ (3 significant figures).
14. 52, 163
π × 2² × 13 = 52π cm³; with the π key, 52π ≈ 163 cm³ = 163 mL (1 cm³ = 1 mL).
15. A → C → B
Put the numbers in V = πr²h, divide both sides by 7π for r² = 9, then take the square root: r = 3 cm.
16. 512 medals
The volume stays: the rod π × 2² × 32 = 128π, each medal π × 1² × 0.25 = 0.25π; 128π ÷ 0.25π = 512. The π cancels: no value needed.
17. 75.4 L
Each second a column of water 100 cm long comes out: π × 1² × 100 = 100π cm³; 4 minutes is 240 seconds, then ÷ 1000 for litres: 24π ≈ 75.4 L.
18. 169 π cm³
The whole cake is π × 13² × 4 = 676π cm³; in 4 slices, 676π ÷ 4 = 169π cm³ each.

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