A cone has base diameter $1$ and slant height $3$ units. From a point $A$ halfway up the side of the cone, a string is passed twice around it to come to a point $B$ on the circumference of the base, directly below $A$. The string is then pulled until taut. How far is it from A to B along this taut string?
Unsure of how to approach this strange looking question, any help would be appreciated.