If the wheel of a bicycle has a diameter of 60 cm, find how far a cyclist will have travelled after the wheel has rotated 100 times.
Answer: One turn = πd = 227 × 60 = 13207 ≈ 188.57 cm. 100 turns ≈ 18 857 cm ≈ 188.57 m.
Step-by-step solution
Idea: In one rotation the wheel rolls forward by its circumference.
- Circumference = πd = 227 × 60 = 13207 ≈ 188.57 cm.1 mark
- Distance = 100 × 13207 = 1320007 ≈ 18 857 cm ≈ 188.57 m.1 mark
The cyclist travels about 18 857 cm, i.e. about 188.57 m.
Answer to write in the exam
One rotation = πd = 227 × 60 = 13207 cm
100 rotations = 1320007 cm ≈ 18857 cm
∴ Distance ≈ 188.57 m
Common mistakes that cost marks
- Using 2π × 60 (treating the diameter as the radius).
- Leaving the answer as 18857.14 without units, or calling it 18.86 m (1 m = 100 cm).
How this can come in the exam
MCQ (1 mark)
A wheel of diameter 1.4 m rotates 50 times. The distance covered is (use π = 227)
- 110 m
- 70 m
- 440 m
- 220 m
Show answer
(D) 220 m
One turn = 227 × 1.4 = 4.4 m; 50 × 4.4 = 220 m.
Try one yourself
A wheel of diameter 35 cm rotates 200 times. How far does it go? (Use π = 227.)
Show answer
227 × 35 = 110 cm per turn; 200 × 110 = 22 000 cm = 220 m.
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