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Circle · wheel rotations
P6 · Circles · PSLE Maths
Question
Mei Ling cycles 1.32 km along the park connector. The diameter of her bicycle wheel is 84 cm. Take π = 22/7. How many complete turns does one wheel make?
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Hint
In 1 turn, the wheel moves forward by its circumference. Find the circumference first, then change 1.32 km to cm.
Show the answer and step-by-step explanation
Answer: Number of turns 500 turns
- One turn — When the wheel makes 1 turn, its rim rolls through one whole round. The diameter given is 84 cm.
- Unroll it — Unroll one round of the wheel into a straight line. The length of this line is the circumference of the circle.
- Find circumference — The distance in one turn is the circumference. Use C = πd, with π = 22/7.
- Same unit — The total distance is 1.32 km. Since one turn is in cm, change the total distance to cm too.
- Divide by one turn — Now ask: how many 264 cm lengths are there in 132000 cm? Use division to find the number of turns.
- Check — Check: 500 turns × 264 cm = 132000 cm = 1.32 km. Correct. Answer: 500 turns. 📌 Key idea: in 1 turn, a wheel travels 1 circumference. Number of turns = total distance ÷ circumference.
Method: Unroll one turn of the wheel into a straight line; its length is the circumference, C = πd. Total distance ÷ distance in one turn = number of turns.
Practice: 3 similar questions
- Ali's scooter wheel has a diameter of 56 cm. After the wheel makes 250 turns, how far has the scooter travelled in m? Take π = 22/7.
Answer
440 m — Distance in 1 turn = circumference = 22/7 × 56 = 176 cm. Distance in 250 turns = 250 × 176 = 44000 cm. 44000 cm = 440 m.
- Siti cycles 770 m to the library. The diameter of her bicycle wheel is 49 cm. Take π = 22/7. How many turns does one wheel make?
Answer
500 turns — Distance in 1 turn = circumference = 22/7 × 49 = 154 cm. 770 m = 77000 cm. Number of turns = 77000 ÷ 154 = 500 turns.
- Raju's bicycle wheel has a diameter of 42 cm. He cycles from Gate A to Gate B and then back to Gate A along the same route. The wheel makes 750 turns in all. Take π = 22/7. What is the one-way distance from Gate A to Gate B in m?
Answer
495 m — Distance in 1 turn = circumference = 22/7 × 42 = 132 cm. Total distance there and back = 750 × 132 = 99000 cm = 990 m. One-way distance = 990 ÷ 2 = 495 m.
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