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Circle Arcs and Length
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Circle Arcs and Length
Use the arc-length formula: arc length = (central angle ÷ 360°) × 2πr. Unless a question says otherwise, use π = 3.14. Show your working for calculation questions.
Arc Basics
1.Which description best defines an arc of a circle?
- A straight segment joining two points on a circle
- A curved section of the circle’s circumference
- A line from the centre to the circumference
- The space enclosed by the circumference
2.Which expression gives the length of an arc when its central angle is θ degrees and the circle has radius r?
- (θ ÷ 360) × 2πr
- (θ ÷ 360) × πr²
- 2πr ÷ θ
- θ × 2πr
3.A circle has a radius of 9 cm. Find the length of the arc subtended by a central angle of 80°. Use π = 3.14.
- 12.56 cm
- 18.84 cm
- 6.28 cm
- 25.12 cm
4.Select all the recognised names for types of arcs.
- Minor arc
- Major arc
- Semicircle
- Radius arc
Arc Length in Context
5.A circular garden has a radius of 5 m. A curved edging section spans a central angle of 72°. What is the length of the edging? Use π = 3.14 and show your calculation.
6.The tip of a 12 cm minute hand travels around a clock face for 20 minutes. How far does it travel along its circular path? Use π = 3.14.
7.A circular running path has a radius of 28 m. A runner completes half of one lap. What distance do they cover along the path? Use π = 3.14.
8.Name two everyday objects or settings where you could identify a curved arc. Give one example of the arc on each.
Stretch Your Thinking
9.A bicycle wheel has a radius of 42 cm. If it turns through 150°, how far does a point on its rim travel along the circumference? Use π = 3.14.
10.For the same circle, what happens to the arc length if the central angle is doubled while the radius stays fixed?
- It stays unchanged
- It doubles
- It becomes half as long
- It becomes four times as long
11.A round flatbread has a radius of 16 cm. Find the length of the curved crust on a slice with a central angle of 135°. Use π = 3.14.
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