Measures and solids · Ages 13–14

Surface area of a cylinder worksheet

Part of: Prisms & 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 radius of 3 cm and a height of 11 cm. What is its total surface area, in terms of π?
Answer:
2.The cylinder in the picture has a base radius of 6 cm and a height of 10 cm. What is its curved surface area, in terms of π?
Answer:
3.The cylinder in the picture has a base radius of 6 cm and a height of 6 cm. What is its total surface area, in terms of π?
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4.The cylinder in the picture has a base radius of 8 cm and a height of 19 cm. What is its curved surface area, in terms of π?
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5.The picture shows a cylindrical cup with no lid, base radius 5 cm, height 3 cm. What is the area of its outside (the base and the side), in terms of π?
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6.Taking π as 3.14, what is the total surface area of the cylinder in the picture, radius 5 cm and height 12 cm, in cm²?
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7.The picture shows a cylindrical cup with no lid, base radius 2 cm, height 12 cm. What is the area of its outside (the base and the side), in terms of π?
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8.The cylinder in the picture has a base radius of 3 cm and a curved surface area of 120π cm². How high is it, in cm?
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9.A cylinder has a base radius of 2 cm and a total surface area of 20π cm². How high is it, in cm?
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10.The cylinder in the picture has a base radius of 10 cm and a curved surface area of 160π cm². How high is it, in cm?
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11.Cut the curved surface of the cylinder in the picture and lay it flat: a rectangle 5 cm wide. How long is the rectangle?
- A. 144π cm
- B. 24 cm
- C. 24π cm
- D. 12π cm
Choose the right answer
Answer:
12.A cylinder of base radius 2 cm and height 3 cm has a total surface area of 16π cm².
True or false?
Answer:

13.A tin of sweetcorn has a base radius of 5 cm and a height of 9 cm. A paper label covers its side exactly (take π as 3.14). What is the label's area, in cm²?
Working:
Answer:
14.A cylinder has a total surface area of 360π cm² and a base radius of 9 cm. Find its height h: put the steps in order.
- A. 18πh = 360π − 162π = 198π
- B. h = 198 ÷ 18 = 11
- C. 2π × 9² + 2π × 9 × h = 360π
- D. 162π + 18πh = 360π
Write the letters in the right order
Working:
Answer:
15.A biscuit tin with no lid, a cylinder of base radius 3 cm and height 18 cm, is made from sheet metal. At least how much metal does it take, in terms of π?
Working:
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16.A paint roller is a cylinder of radius 8 cm and width 34 cm. One turn of the roller paints π cm²; 8 turns paint π cm².
Fill in each blank
Working:
Answer:
17.A workshop is to paint the outside of 12 cylindrical pipes against rust. Each pipe is 50 cm across the outside and 2 m long (take π as 3.14). The paint costs $10 a square metre. How many dollars does it cost in all?
Working:
Answer:
18.A big drum is a cylinder 36 cm across and 41 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?
Working:
Answer:

Show the answers and working

Surface area of a cylinder worksheet: Answers and working

1. 84 π cm²
Curved 2π × 3 × 11 = 66π, the two ends 2 × π × 3² = 18π, 84π cm² in all.
2. 120 π cm²
Opened out the curved surface is a rectangle, the circumference 2π × 6 = 12π long and the height 10 wide: 12π × 10 = 120π cm².
3. 144 π cm²
Curved 2π × 6 × 6 = 72π, the two ends 2 × π × 6² = 72π, 144π cm² in all.
4. 304 π cm²
Opened out the curved surface is a rectangle, the circumference 2π × 8 = 16π long and the height 19 wide: 16π × 19 = 304π cm².
5. 55 π cm²
No lid, so one end only: π × 5² = 25π, plus the curved surface 2π × 5 × 3 = 30π: 55π cm².
6. 533.8 cm²
In π: 2π × 5² + 2π × 5 × 12 = 170π; then 3.14 at the end: 170 × 3.14 = 533.8 cm².
7. 52 π cm²
No lid, so one end only: π × 2² = 4π, plus the curved surface 2π × 2 × 12 = 48π: 52π cm².
8. 20 cm
Curved area = circumference × height: 2π × 3 = 6π, so the height = 120π ÷ 6π = 20 cm.
9. 3 cm
The ends are 2π × 2² = 8π, so the curved surface is 20π − 8π = 12π; height = 12π ÷ (2π × 2) = 12 ÷ 4 = 3 cm.
10. 8 cm
Curved area = circumference × height: 2π × 10 = 20π, so the height = 160π ÷ 20π = 8 cm.

11. C. 24π cm
Rolled up, the rectangle goes once round the base: the circumference, 2π × 12 = 24π cm.
12. False
Two ends 2π × 2² and the curved surface 2π × 2 × 3: 20π cm².

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

13. 282.6 cm²
The label is the curved surface, a rectangle when flat: 2 × 3.14 × 5 × 9 = 282.6 cm². The top and bottom aren't covered.
14. C → D → A → B
Put the numbers in, work out the ends, 162π, move them across for the curved surface 198π, then divide by 18π: h = 11 cm.
15. 117 π cm²
One base π × 3² = 9π and the curved side 2π × 3 × 18 = 108π: 117π cm². The lid isn't part of it.
16. 544, 4352
One turn prints the curved surface once: 2π × 8 × 34 = 544π; 8 turns make 544π × 8 = 4352π.
17. 376.8 dollars
Same units first: 50 cm across = 50 ÷ 100 m. One pipe's curved surface, 3.14 × diameter × length = 3.14 m², 12 of them 37.68 m², times $10: $376.8.
18. 648 π cm²
The skin is two circles: radius 36 ÷ 2 = 18 cm, 2 × π × 18² = 648π cm². The side is the curved surface, not skin: the height isn't needed.

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