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Circle Arcs and Length
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Circle Arcs and Length
📚 Part 1: Understanding Arcs
1. What is an arc?
A straight line through a circle
A continuous part of the circumference of a circle
The centre point of a circle
Half the diameter of a circle
2. Which formula is used to calculate arc length?
Arc length = πr²
Arc length = 2πr
Arc length = (θ/360°) × 2πr
Arc length = θ × r
3. A circle has a radius of 6 cm and a central angle of 120°. What is the arc length? (Use π = 3.14)
12.56 cm
6.28 cm
25.12 cm
18.84 cm
4. Which of these are types of arcs? (Select all that apply)
Minor arc
Major arc
Semicircle
Radius arc
✏️ Part 2: Real-World Applications
5. Playground Problem: A circular merry-go-round has a radius of 3 metres. A safety rail forms an arc with a central angle of 90°. Calculate the length of the safety rail. Show your working.
Answer: _____________ metres
6. Clock Problem: A clock's minute hand is 8 cm long. How far does the tip of the hand travel in 15 minutes? (Remember: the minute hand moves 360° in 60 minutes)
Answer: _____________ cm
7. Sports Track: A circular running track has a radius of 40 metres. If a runner completes three-quarters of the track, what distance did they run along the arc?
Answer: _____________ metres
8. Explain in your own words where you might see arcs in everyday life. Give at least two examples.
🎯 Part 3: Challenge Questions
9. A bicycle wheel has a radius of 35 cm. If the wheel rotates through an angle of 240°, how far does the bicycle move forward?
Answer: _____________ cm
10. Complete this statement: "If the central angle doubles, the arc length __________"
stays the same
doubles
halves
quadruples
11. A pizza slice has a central angle of 45° and the pizza has a radius of 20 cm. What is the length of the crust (arc) on this slice?
Answer: _____________ cm
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