Measures and solids · Ages 13–14
Surface area of a cylinder worksheet
Part of: Cylinders
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Surface area of a cylinder worksheet
Measures and solids · Ages 13–14
Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The cylinder in the picture has a base radius of 6 cm and a height of 10 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 17 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 13 cm. What is its total surface area, in terms of π?
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4.Using your calculator's π key, what is the total surface area of the cylinder in the picture, radius 6 cm and height 11 cm, in cm², to 3 significant figures?
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5.The picture shows a cylindrical cup with no lid, base radius 3 cm, height 10 cm. What is the area of its outside (the base and the side), in terms of π?
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6.A cylinder of base radius 1 cm and height 2 cm is glued centred on top of a cylinder of base radius 6 cm and height 5 cm, making one solid. In terms of π, what is the solid's total surface area, in cm²?
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7.A rectangle of paper 14π cm long and 14 cm wide is rolled up along its length into a cylindrical can's side, edge to edge, and given a base. In terms of π, what is the can's capacity, in cm³?
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8.The cylinder in the picture has a base radius of 11 cm and a curved surface area of 88π cm². How high is it, in cm?
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9.A cylinder has a base radius of 5 cm and a total surface area of 170π cm². How high is it, in cm?
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10.A rectangle of paper 18π cm long and 11 cm wide is rolled up along its length into a cylindrical can's side, edge to edge, and given a base. In terms of π, what is the can's capacity, in cm³?
Answer:
Part B: Choose, or true or false (2 marks each)
11.Cut the curved surface of the cylinder in the picture and lay it flat: a rectangle 7 cm wide. How long is the rectangle?
- A. 12 cm
- B. 6π cm
- C. 12π cm
- D. 36π cm
Choose the right answer
Answer:
12.A cylinder of base radius 2 cm and height 16 cm has a total surface area of 72π cm².
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A biscuit tin with no lid, a cylinder of base radius 9 cm and height 14 cm, is made from sheet metal. At least how much metal does it take, in terms of π?
Working:
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14.A paint roller is a cylinder of radius 10 cm and width 41 cm. One turn of the roller paints π cm²; 22 turns paint π cm².
Fill in each blank
Working:
Answer:
15.A tin of sweetcorn has a base radius of 3 cm and a height of 12 cm. A paper label covers its side exactly. Using your calculator's π key, what is the label's area, in cm², to 3 significant figures?
Working:
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16.A two-tier round cake: the top tier, base radius 4 cm and 5 cm high, sits centred on the bottom tier, base radius 8 cm and 3 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
Working:
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17.A big drum is a cylinder 40 cm across and 34 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:
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18.A workshop is to paint the outside of 4 cylindrical pipes against rust. Each pipe is 40 cm across the outside and 4 m long. The paint costs $50 a square metre. Using your calculator's π key, how many dollars does it cost in all, to the nearest dollar?
Working:
Answer:
Show the answers and working
Surface area of a cylinder worksheet: Answers and working
Part A: Working out and filling in
1. 192 π cm²
Curved 2π × 6 × 10 = 120π, the two ends 2 × π × 62 = 72π, 192π cm² in all.
2. 204 π cm²
Opened out the curved surface is a rectangle, the circumference 2π × 6 = 12π long and the height 17 wide: 12π × 17 = 204π cm².
3. 228 π cm²
Curved 2π × 6 × 13 = 156π, the two ends 2 × π × 62 = 72π, 228π cm² in all.
4. 641 cm²
In π: 2π × 62 + 2π × 6 × 11 = 204π; press π at the end: 204π ≈ 641 cm² (3 significant figures).
5. 69 π cm²
No lid, so one end only: π × 32 = 9π, plus the curved surface 2π × 3 × 10 = 60π: 69π cm².
6. 136 π cm²
Two curved surfaces: 2π × 1 × 2 = 4π and 2π × 6 × 5 = 60π. Seen from above, the top of the small one and the ring of the big one left showing make one circle of radius 6; with the bottom, 2 × π × 62 = 72π. 136π cm² in all.
7. 686 π cm³
The paper's length becomes the base's circumference: 2πr = 14π, so r = 7 cm; its width is the height, 14 cm. Capacity π × 72 × 14 = 686π cm³.
8. 4 cm
Curved area = circumference × height: 2π × 11 = 22π, so the height = 88π ÷ 22π = 4 cm.
9. 12 cm
The ends are 2π × 52 = 50π, so the curved surface is 170π − 50π = 120π; height = 120π ÷ (2π × 5) = 120 ÷ 10 = 12 cm.
10. 891 π cm³
The paper's length becomes the base's circumference: 2πr = 18π, so r = 9 cm; its width is the height, 11 cm. Capacity π × 92 × 11 = 891π cm³.
Part B: Choose, or true or false
11. C. 12π cm
Rolled up, the rectangle goes once round the base: the circumference, 2π × 6 = 12π cm.
12. True
Two ends 2π × 22 and the curved surface 2π × 2 × 16: 72π cm².
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 333 π cm²
One base π × 92 = 81π and the curved side 2π × 9 × 14 = 252π: 333π cm². The lid isn't part of it.
14. 820, 18040
One turn prints the curved surface once: 2π × 10 × 41 = 820π; 22 turns make 820π × 22 = 18040π.
15. 226 cm²
The label is the curved surface, a rectangle when flat: 2π × 3 × 12 = 72π ≈ 226 cm². The top and bottom aren't covered.
16. 88, 64, 152
Curved sides 2π × 4 × 5 + 2π × 8 × 3 = 88π. The top tier's top and the bottom tier's ring, seen from above, make one circle of radius 8: 64π. No icing underneath: 88π + 64π = 152π cm².
17. 800 π cm²
The skin is two circles: radius 40 ÷ 2 = 20 cm, 2 × π × 202 = 800π cm². The side is the curved surface, not skin: the height isn't needed.
18. 1005 dollars
Same units first: 40 cm across = 0.4 m. One pipe's curved surface, π × diameter × length = 1.6π m², 4 of them 6.4π m², times $50, with the π key: about $1,005.
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