A wheel with radius $1 \mathrm{~m}$ is rolled in a straight line through one complete revolution on a flat horizontal surface. How many metres did the centre of the wheel travel horizontally from its starting location?
(A) $4 \pi$
(B) 2
(C) $2 \pi$
(D) $\pi$
(E) 1
We begin by considering a point $P$ which is where the circle first touches a line $L$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-347.jpg?height=193&width=686&top_left_y=1481&top_left_x=774)

If a circle makes one complete revolution, the point $P$ moves to $P^{\prime}$ and the distance $P P^{\prime}$ is the circumference of the circle, or $2 \pi \mathrm{m}$.

If we now complete the rectangle, we can see that the distance the centre travels is $C C^{\prime}$ which is exactly equal to $P P^{\prime}$ or $2 \pi \mathrm{m}$.

ANSWER: (C)