Two round garden rollers, each of radius 14 cm, are placed touching each other on a flat lawn, with their centres P and Q on a straight line. The rollers are then rolled along the lawn in opposite directions, away from each other. Each roller makes exactly 3 complete turns and stops. Find the distance between the centres P and Q after the turns. (Take π = 227.)
Need a hint?
Work out how far one roller travels in 3 turns first. Then remember the rollers started touching, so their centres were 28 cm apart, and both move away from each other.
Worked answer
- Circumference of one roller = 2 × 227 × 14 = 88 cm.
- Distance rolled by one roller = 3 × 88 = 264 cm.
- Distance between centres at the start = 14 + 14 = 28 cm.
- Distance between centres after the turns = 28 + 264 + 264 = 556 cm.
The mistake this question tests
Radius and diameter in circles
Pupils often use the radius as if it were the circumference, or forget that the rollers began 28 cm apart and only add the distance rolled.
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