Measures and solids · Ages 13–14

Volume of a cylinder worksheet

Part of: Prisms & cylinders

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Measures and solids · Ages 13–14

Numsprite
numsprite.com

Name:Date:Score:／48

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 12 cm. What is its volume, in terms of π?
Answer:
2.The cylinder in the picture has a base radius of 3 cm and a height of 4 cm. What is its volume, in terms of π?
Answer:
3.The cylinder in the picture has a base radius of 7 cm and a height of 19 cm. What is its volume, in terms of π?
Answer:
4.The cylinder in the picture has a volume of 637π cm³ and a base radius of 7 cm. How high is it, in cm?
Answer:
5.Taking π as 3.14, find the volume of the cylinder in the picture: radius 10 cm, height 13 cm. What is it, in cm³?
Answer:
6.The cylinder in the picture has a volume of 224π cm³ and a base radius of 4 cm. How high is it, in cm?
Answer:
7.The cylinder in the picture has a volume of 486π cm³ and a height of 6 cm. What is its base radius r, in cm?
Answer:
8.Cylinder A's radius is 2 times cylinder B's, but A is only 13 as high as B. How many times B's volume is A's?
Answer in simplest form
Answer:
9.Cylinder A's radius is 2 times cylinder B's, but A is only 14 as high as B. How many times B's volume is A's?
Answer in simplest form
Answer:

10.The cylinder in the picture is 18 cm across and 20 cm high. What is its volume?
- A. 180π cm³
- B. 1620π cm³
- C. 6480π cm³
- D. 360π cm³
Choose the right answer
Answer:
11.The cylinder in the picture is 16 cm across and 9 cm high. What is its volume?
- A. 72π cm³
- B. 2304π cm³
- C. 576π cm³
- D. 144π cm³
Choose the right answer
Answer:
12.A cylinder 16 cm across and 4 cm high has a volume of 256π cm³.
True or false?
Answer:

13.A round cake of radius 12 cm and height 5 cm is cut from the centre into 6 equal slices. What is each slice's volume, in terms of π?
Working:
Answer:
14.A can of soda is a cylinder of base radius 4 cm and height 13 cm. Its capacity in terms of π is π cm³; taking π as 3.14, about mL.
Fill in each blank
Working:
Answer:
15.A cylindrical flowerpot holds 1210π cm³ and is 10 cm high. Find its base radius: put the steps in order.
- A. πr² × 10 = 1210π
- B. r = 121 = 11
- C. r² = 1210 ÷ 10 = 121
Write the letters in the right order
Working:
Answer:
16.A cylindrical water tank on a roof has a base radius of 3 m and a height of 2 m (take π as 3.14). What is its capacity, in m³?
Working:
Answer:
17.A hose has an inner radius of 1 cm, and the water in it moves 75 cm every second (take π as 3.14). How many litres flow out in 4 minutes?
Working:
Answer:
18.A metal rod, a cylinder of radius 6 cm and length 11 cm, is melted down and cast into round medals, cylinders of radius 1 cm and 0.5 cm thick, with nothing lost. How many medals can be made?
Working:
Answer:

Show the answers and working

Volume of a cylinder worksheet: Answers and working

1. 48 π cm³
The radius is half the diameter, 4 ÷ 2 = 2 cm; volume π × 2² × 12 = 48π cm³.
2. 36 π cm³
Base area π × 3² = 9π cm², volume = base area × height = 9π × 4 = 36π cm³.
3. 931 π cm³
Base area π × 7² = 49π cm², volume = base area × height = 49π × 19 = 931π cm³.
4. 13 cm
The base area is π × 7² = 49π cm², so the height = volume ÷ base area = 637π ÷ 49π = 13 cm.
5. 4082 cm³
Work in π first: π × 10² × 13 = 1300π, then put the value in at the end: 1300 × 3.14 = 4082 cm³.
6. 14 cm
The base area is π × 4² = 16π cm², so the height = volume ÷ base area = 224π ÷ 16π = 14 cm.
7. 9 cm
πr² × 6 = 486π, so r² = 486 ÷ 6 = 81 and r = 9 cm (9 × 9 = 81).
8. 43 times
Volume πr²h: 2 times the radius makes r² 4 times; 13 the height, so 4 × 13 = 43 times the volume.
9. 1 time
Volume πr²h: 2 times the radius makes r² 4 times; 14 the height, so 4 × 14 = 1 times the volume.

10. B. 1620π cm³
The radius is 18 ÷ 2 = 9 cm, so the volume is π × 9² × 20 = 1620π cm³.
11. C. 576π cm³
The radius is 16 ÷ 2 = 8 cm, so the volume is π × 8² × 9 = 576π cm³.
12. True
The radius is 8 cm, so the volume is π × 8² × 4 = 256π cm³.

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

13. 120 π cm³
The whole cake is π × 12² × 5 = 720π cm³; in 6 slices, 720π ÷ 6 = 120π cm³ each.
14. 208, 653.12
π × 4² × 13 = 208π cm³; 208 × 3.14 = 653.12 cm³ = 653.12 mL (1 cm³ = 1 mL).
15. A → C → B
Put the numbers in V = πr²h, divide both sides by 10π for r² = 121, then take the square root: r = 11 cm.
16. 56.52 m³
In π: π × 3² × 2; then times 3.14: 56.52 m³.
17. 56.52 L
Each second a column of water 75 cm long comes out: 3.14 × 1² × 75 cm³; times 60 × 4 seconds, then ÷ 1000 for litres: 56.52 L.
18. 792 medals
The volume stays: the rod π × 6² × 11 = 396π, each medal π × 1² × 0.5 = 0.5π; 396π ÷ 0.5π = 792. The π cancels: no value needed.

Numsprite · numsprite.com/en/worksheets/prisms-and-cylinders/volume-of-cylinders