PK 2017 Q4
4. A circle of radius 1 rolls along a straight line from the point \(K\) to the point \(L\), where \(KL = 11\pi\). Which of the following pictures shows the correct appearance of the circle when it reaches \(L\)?
Pink Kangaroo 2017, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D
The circumference is \(2\pi\), so every time the circle rolls \(2\pi\) it has turned 360° and looks the same as it did at \(K\). After \(11\pi\), it has turned 5 ½ turns, which is picture D.
Solution © UK Mathematics Trust, from the PK 2017 solutions.