Measures and solids · Ages 13–14

Cylinders worksheet

Covers: Volume of a cylinder, Surface area of a cylinder, Cylinders at work

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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 radius of 2 cm and a height of 10 cm. What is its volume, in terms of π?
Answer:
2.Using your calculator's π key, find the volume of the cylinder in the picture: radius 8 cm, height 10 cm. To 3 significant figures, what is it, in cm³?
Answer:
3.The cylinder in the picture has a volume of 1024π cm³ and a base radius of 8 cm. How high is it, in cm?
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4.The cylinder in the picture has a base radius of 8 cm and a height of 6 cm. What is its total surface area, in terms of π?
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5.Using your calculator's π key, what is the total surface area of the cylinder in the picture, radius 3 cm and height 12 cm, in cm², to 3 significant figures?
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6.The picture shows a cylindrical cup with no lid, base radius 5 cm, height 17 cm. What is the area of its outside (the base and the side), in terms of π?
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7.The hollow cylinder in the picture (a length of pipe) has an outer radius of 9 cm and an inner radius of 7 cm, and is 12 cm long. What is the volume of the pipe itself, in terms of π?
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8.The cylindrical container in the picture has a base radius of 10 cm and water 5 cm deep. A stone is dropped in and sinks right under, and the water rises 3 cm. What is the stone's volume, in terms of π?
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9.1100 mL of water is poured into an empty cylindrical cup of base radius 8 cm. Using your calculator's π key, how deep is the water, in cm, to 3 significant figures?
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10.A cylinder 16 cm across and 6 cm high has a volume of 384π cm³.
True or false?
Answer:
11.A cylinder of base radius 7 cm and height 7 cm has a total surface area of 147π cm².
True or false?
Answer:
12.A cylindrical container of base radius 5 cm has some water in it. 225π cm³ more is poured in, none spilling. How far does the water rise?
- A. 9 cm
- B. 225π ÷ (2π × 5) cm
- C. 225 cm
- D. 225π ÷ 5π cm
Choose the right answer
Answer:

13.A round cake of radius 12 cm and height 8 cm is cut from the centre into 4 equal slices. What is each slice's volume, in terms of π?
Working:
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14.A metal rod, a cylinder of radius 3 cm and length 22 cm, is melted down and cast into round medals, cylinders of radius 2 cm and 0.5 cm thick, with nothing lost. How many medals can be made?
Working:
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15.A two-tier round cake: the top tier, base radius 3 cm and 7 cm high, sits centred on the bottom tier, base radius 7 cm and 4 cm high. Everything outside but the bottom is iced. In terms of π: the two curved sides make π cm², all the faces looking up (the top tier's top and the ring of the bottom tier left showing) π cm², and the area iced π cm².
Fill in each blank
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16.A big drum is a cylinder 46 cm across and 39 cm high, with skin stretched over its top and bottom and its side painted. In terms of π, how many cm² of skin are there?
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17.A cylindrical flask is 3 cm in base radius and 11 cm high inside. Its capacity in terms of π is π cm³; with your calculator's π key, to the nearest mL, it holds about mL of hot water.
Fill in each blank
Working:
Answer:
18.A florist's cylindrical bucket has a base radius of 9 cm, with water 5 cm deep. A solid cylinder of flower foam, base radius 6 cm and 25 cm high, is stood upright on the bucket's floor; it rises above the water, and none spills. In terms of π, how many cm² of the foam's side are wet?
Working:
Answer:

Show the answers and working

Cylinders worksheet: Answers and working

1. 40 π cm³
Base area π × 2² = 4π cm², volume = base area × height = 4π × 10 = 40π cm³.
2. 2010 cm³
Work in π first: π × 8² × 10 = 640π, then press π at the end: 640π ≈ 2010 cm³ (3 significant figures).
3. 16 cm
The base area is π × 8² = 64π cm², so the height = volume ÷ base area = 1024π ÷ 64π = 16 cm.
4. 224 π cm²
Curved 2π × 8 × 6 = 96π, the two ends 2 × π × 8² = 128π, 224π cm² in all.
5. 283 cm²
In π: 2π × 3² + 2π × 3 × 12 = 90π; press π at the end: 90π ≈ 283 cm² (3 significant figures).
6. 195 π cm²
No lid, so one end only: π × 5² = 25π, plus the curved surface 2π × 5 × 17 = 170π: 195π cm².
7. 384 π cm³
The cross-section is a ring: π × 9² − π × 7² = 32π cm²; volume 32π × 12 = 384π cm³.
8. 300 π cm³
The stone's volume equals the water it lifts: base area π × 10² = 100π, times the 3 cm rise: 300π cm³. The water's first depth isn't needed.
9. 5.47 cm
1100 mL = 1100 cm³; the base is π × 8² = 64π cm², so the depth = 1100 ÷ 64π ≈ 5.47 cm (3 significant figures).

10. True
The radius is 8 cm, so the volume is π × 8² × 6 = 384π cm³.
11. False
Two ends 2π × 7² and the curved surface 2π × 7 × 7: 196π cm².
12. A. 9 cm
The water poured in is a cylinder on the container's base: rise = 225π ÷ (π × 5²) = 225 ÷ 25 = 9 cm.

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

13. 288 π cm³
The whole cake is π × 12² × 8 = 1152π cm³; in 4 slices, 1152π ÷ 4 = 288π cm³ each.
14. 99 medals
The volume stays: the rod π × 3² × 22 = 198π, each medal π × 2² × 0.5 = 2π; 198π ÷ 2π = 99. The π cancels: no value needed.
15. 98, 49, 147
Curved sides 2π × 3 × 7 + 2π × 7 × 4 = 98π. The top tier's top and the bottom tier's ring, seen from above, make one circle of radius 7: 49π. No icing underneath: 98π + 49π = 147π cm².
16. 1058 π cm²
The skin is two circles: radius 46 ÷ 2 = 23 cm, 2 × π × 23² = 1058π cm². The side is the curved surface, not skin: the height isn't needed.
17. 99, 311
π × 3² × 11 = 99π cm³; with the π key, 99π ≈ 311 cm³, which is about 311 mL.
18. 108 π cm²
The new depth first: the water, π × 9² × 5 = 405π, keeps its volume but fills only the ring round the foam, π(9² − 6²) = 45π, so it is 405π ÷ 45π = 9 cm deep. The wet side is a curved surface 9 cm high: 2π × 6 × 9 = 108π cm².

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