Measures and solids · Ages 14–15

Surface area of a sphere worksheet

Part of: Cones & spheres

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Measures and solids · Ages 14–15

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

1.The sphere in the picture has a radius of 20 cm. What is its surface area, in terms of π?
Answer:
2.Taking π as 3.14, what is the surface area of the sphere in the picture (radius 5 cm), in cm²?
Answer:
3.Taking π as 3.14, what is the surface area of the sphere in the picture (radius 20 cm), in cm²?
Answer:
4.The sphere in the picture is 16 cm across. What is its surface area, in terms of π?
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5.The sphere in the picture has a surface area of 1156π cm². What is its radius, in cm?
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6.The sphere in the picture is 12 cm across. What is its surface area, in terms of π?
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7.A hollow hemispherical bowl has an outer radius of 11 cm and an inner radius of 3 cm, its rim a flat ring. What is its total surface area (outside, inside and rim), in terms of π?
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8.A sphere has a surface area of 576π cm². What is its volume, in terms of π?
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9.A sphere has a surface area of 324π cm². What is its volume, in terms of π?
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10.The solid hemisphere in the picture has a radius of 15 cm. What is its total surface area?
- A. 225π cm²
- B. 450π cm²
- C. 675π cm²
- D. 900π cm²
Choose the right answer
Answer:
11.A solid hemisphere of radius 16 cm has a total surface area of 768π cm².
True or false?
Answer:
12.A solid hemisphere of radius 17 cm has a total surface area of 867π cm².
True or false?
Answer:

13.A hemispherical dome has a radius of 4 m, and its curved outside is to be painted at $60 a square metre. Taking π as 3.14, how much does it cost, in dollars?
Working:
Answer:
14.A globe has a radius of 11 cm. The map on its surface is π cm² in terms of π, and cm² taking π as 3.14.
Fill in each blank
Working:
Answer:
15.A workshop makes 20 balls of radius 6 cm, each covered in leather. In terms of π, how many cm² of leather does it need in all?
Working:
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16.A solid glass paperweight, a hemisphere of radius 8 cm, has film stuck over its whole surface. The curved part takes π cm², the flat part π cm², π cm² in all.
Fill in each blank
Working:
Answer:
17.A solid glass paperweight, a hemisphere of radius 11 cm, has film stuck over its whole surface. The curved part takes π cm², the flat part π cm², π cm² in all.
Fill in each blank
Working:
Answer:
18.A hemispherical dome has a radius of 13 m, and its curved outside is to be painted at $55 a square metre. Taking π as 3.14, how much does it cost, in dollars?
Working:
Answer:

Show the answers and working

Surface area of a sphere worksheet: Answers and working

1. 1600 π cm²
4πr² = 4 × π × 20² = 1600π cm²: 4 circles of radius 20.
2. 314 cm²
4 × 3.14 × 5² = 314 cm².
3. 5024 cm²
4 × 3.14 × 20² = 5024 cm².
4. 256 π cm²
Radius 8: 4 × π × 8² = 256π cm² (that is, π × diameter²).
5. 17 cm
4πr² = 1156π, so r² = 1156 ÷ 4 = 289 and r = 17 cm.
6. 144 π cm²
Radius 6: 4 × π × 6² = 144π cm² (that is, π × diameter²).
7. 372 π cm²
Outside 2π × 11² = 242π, inside 2π × 3² = 18π, rim π(11² − 3²) = 112π: 372π cm² in all.
8. 2304 π cm³
4πr² = 576π, so r = 12; volume 43 × π × 12³ = 2304π cm³.
9. 972 π cm³
4πr² = 324π, so r = 9; volume 43 × π × 9³ = 972π cm³.

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

13. 6028.8 dollars
The curved part 2 × 3.14 × 4² = 100.48 m² (no base to paint); × $60 = $6,028.8.
14. 484, 1519.76
4 × π × 11² = 484π; × 3.14 = 1519.76.
15. 2880 π cm²
Each is 4 × π × 6²; 20 of them, 2880π cm².
16. 128, 64, 192
Curved 2π × 8² = 128π, flat π × 8² = 64π, 192π in all.
17. 242, 121, 363
Curved 2π × 11² = 242π, flat π × 11² = 121π, 363π in all.
18. 58372.6 dollars
The curved part 2 × 3.14 × 13² = 1061.32 m² (no base to paint); × $55 = $58,372.6.

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