Measures and solids · Ages 14–15

Perimeter of a sector worksheet

Part of: Arc lengths & sectors

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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 sector in the picture has a radius of 2 cm and an angle of 90°. Its arc is π cm, and its perimeter (π + ) cm.
Fill in each blank
Answer:
2.Taking π as 3.14, what is the perimeter of the semicircle in the picture (radius 23 cm), in cm?
Answer:
3.The sector in the picture has a radius of 3 cm and an angle of 240°. Its arc is π cm, and its perimeter (π + ) cm.
Fill in each blank
Answer:
4.The sector in the picture has a radius of 5 cm and an angle of 155°. Correct to 1 decimal place, what is its perimeter, in cm?
Answer:
5.Taking π as 3.14, what is the perimeter of the sector in the picture (radius 7 cm, angle 270°), in cm?
Answer:
6.A sector's perimeter is (8π + 40) cm. What is its angle at the centre, in degrees?
Answer:
7.Taking π as 3.14, a sector with an angle of 90° has a perimeter of 82.11 cm. What is its radius, in cm?
Answer:
8.A sector's perimeter is (13π + 26) cm. What is its angle at the centre, in degrees?
Answer:

9.The sector in the picture has a radius of 14 cm and an angle of 270°. What is its perimeter?
- A. (21π + 14) cm
- B. (21π × 28) cm
- C. 21π cm
- D. (21π + 28) cm
Choose the right answer
Answer:
10.The sector in the picture has a radius of 6 cm and an angle of 300°. What is its perimeter?
- A. (10π + 12) cm
- B. 10π cm
- C. (10π + 6) cm
- D. (10π × 12) cm
Choose the right answer
Answer:
11.Taking π as 3.14, a sector of radius 7 cm and angle 180° has a perimeter of 35.98 cm.
True or false?
Answer:
12.Taking π as 3.14, a sector of radius 9 cm and angle 30° has a perimeter of 22.71 cm.
True or false?
Answer:

13.A garden is a sector of radius 3 m with an angle of 120°, to be fenced all round. Taking π as 3.14, the curved part is m, and the fence m in all.
Fill in each blank
Working:
Answer:
14.A round cake of radius 15 cm is cut into 12 equal pieces, and each piece has a ribbon tied right round its edge. Correct to 1 decimal place, how many cm of ribbon does a piece need?
Working:
Answer:
15.A wire 34 cm long is bent exactly into the edge of a sector of radius 9 cm. To the nearest degree, what is the sector's angle at the centre?
Working:
Answer:
16.A running track is two straights of 115 m with a semicircle of radius 27 m at each end. Taking π as 3.14, how many metres is one lap of the inside edge?
Working:
Answer:
17.A round cake of radius 16 cm is cut into 6 equal pieces, and each piece has a ribbon tied right round its edge. Correct to 1 decimal place, how many cm of ribbon does a piece need?
Working:
Answer:
18.A wire 58 cm long is bent exactly into the edge of a sector of radius 15 cm. To the nearest degree, what is the sector's angle at the centre?
Working:
Answer:

Show the answers and working

Perimeter of a sector worksheet: Answers and working

1. 1, 1, 4
Arc 90360 × 2π × 2 = 1π; the perimeter adds two radii, 2 × 2 = 4.
2. 118.22 cm
The semicircle's arc π × 23 = 72.22, plus the diameter 46: 118.22 cm.
3. 4, 4, 6
Arc 240360 × 2π × 3 = 4π; the perimeter adds two radii, 2 × 3 = 6.
4. 23.5 cm
The arc 155360 × 2π × 5 plus the two radii 2 × 5, rounded only at the end: about 23.5 cm.
5. 46.97 cm
The arc 10.5π = 32.97 cm, plus two radii 14 cm: 46.97 cm.
6. 72°
The 40 is the two radii, so r = 20 cm; the arc 8π = θ360 × 2π × 20, so θ = 8 × 180 ÷ 20 = 72°.
7. 23 cm
Perimeter = 90360 × 2 × 3.14 × r + 2r = 3.57r, so r = 82.11 ÷ 3.57 = 23 cm.
8. 180°
The 26 is the two radii, so r = 13 cm; the arc 13π = θ360 × 2π × 13, so θ = 13 × 180 ÷ 13 = 180°.

9. D. (21π + 28) cm
Perimeter = arc + 2 radii = 21π + 28 cm.
10. A. (10π + 12) cm
Perimeter = arc + 2 radii = 10π + 12 cm.
11. True
Perimeter = arc + two radii = 35.98 cm; the arc alone leaves out 2 × 7.
12. True
Perimeter = arc + two radii = 22.71 cm; the arc alone leaves out 2 × 9.

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

13. 6.28, 12.28
The arc 120360 × 2 × 3.14 × 3 = 6.28 m, plus two radii 2 × 3: 12.28 m.
14. 37.9 cm
Each piece is a 30° sector: the arc 2π × 15 ÷ 12, plus the two radii 2 × 15: about 37.9 cm.
15. 102°
The two radii take 2 × 9, so the arc = 34 − 2 × 9 = 16 cm; θ = 16 ÷ (2π × 9) × 360 ≈ 102°.
16. 399.56 m
The two semicircles make a circle: 2 × 3.14 × 27 = 169.56 m, plus the straights 230 m: 399.56 m.
17. 48.8 cm
Each piece is a 60° sector: the arc 2π × 16 ÷ 6, plus the two radii 2 × 16: about 48.8 cm.
18. 107°
The two radii take 2 × 15, so the arc = 58 − 2 × 15 = 28 cm; θ = 28 ÷ (2π × 15) × 360 ≈ 107°.

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