Sample Problem

A male ant is at A, the bottom of the cylinder, and sees a beautiful female ant directly above at B, the top of the cylinder. The cylinder has height 3 m and circumference 4 m. The male ant crawls completely around the cylinder to B. What is the shortest distance it must travel to get to the female ant?



To find the shortest distance, we can unfold the lateral face into a rectangle. The rectangle has side lengths of the height and circumference of the cylinder, which are 3 and 4. The shortest distance between A and B is the diagonal of the rectangle, so we wish to find that length.

By the Pythagorean Theorem, we have 32 + 42 = x2, so 9 + 16 = 25 = x2 and so AB = 5 m.