The wheel of a car has an outer radius of 28 cm. Calculate how far the car travels after one complete turn of the wheel, and how many times the wheel turns during a journey of 1 km.

Step-by-step solution

Idea: Each turn rolls out one circumference; number of turns = distance ÷ circumference, in the same unit.

1. Distance in one turn = 2πr = 2 × 227 × 28 = 176 cm.1 mark
2. 1 km = 1000 m = 100 000 cm.½ mark
3. Number of turns = 100000176 = 568.18… So the wheel turns about 568 times (568 complete turns and a little more).1½ marks

Check: 568 × 176 = 99 968 cm, just under 1 km ✓.

Answer to write in the exam

Common mistakes that cost marks

• Using πd with d = 28 (28 cm is the radius).
• Converting 1 km to 1000 cm or 10 000 cm.

How this can come in the exam

Try one yourself

A wheel has radius 42 cm. How many turns does it make in 2.64 km? (Use π = 227.)

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