Question 3
We have a cylinder with a radius of $1$ cm and a height of $4$ cm. While the point $P$ lies on the bottom circle of the cylinder, the point $Q$ lies on the top circle right above $P$. A string connecting the point $P$ and $Q$ makes a complete turn round the cylinder (see the picture). How long is the shortest such string in cm?
(A) $2\pi$
(B) $4\pi$
(C) $\pi\sqrt{2}$
(D) $2\sqrt{\pi^2 + 4}$
(A) $2\pi$
(B) $4\pi$
(C) $\pi\sqrt{2}$
(D) $2\sqrt{\pi^2 + 4}$