# Distance across cylinder

A cylinder with height 8 and radius 4. An ant walks across this cylinder along the shortest path on the curved surface from the top corner to the bottom corner on the other side (opposite side of the cylinder). What is the distance that the ant travels?

• Unroll. Trace. Calculate. Profit. – Pedro Tamaroff Mar 23 '12 at 2:28

Your cylinder can be thought of as a rolled up rectangle, with height $8$ and width $8\pi$. So your distance will be $\sqrt{(8^2)+(4\pi)^2}.$

Edited: Misread the problem in the first go. Since the ant will end up on the opposite side in the bottom, he is going "down 8" and "over $4\pi$."

• that is not one of the answers – Daniel Mar 21 '12 at 20:08
• As I read the question, it only walks half way around the circle. – Ross Millikan Mar 21 '12 at 20:09
• Daniel, maybe you would care to include the question in its entirety ??? – The Chaz 2.0 Mar 21 '12 at 20:11
• coul,d it be 4 root pi^2+4 – Daniel Mar 21 '12 at 20:12
• I edited my response. I slightly misread the original problem. – user21725 Mar 21 '12 at 20:14

Hint: you can cut the cylinder with a vertical line and unroll it to make it flat. Now what is the shortest path? How long is it?

• is the answer 16? – Daniel Mar 21 '12 at 20:06
• i worked it out to be 4 root pi^2+4 – Daniel Mar 21 '12 at 20:11
• @Daniel: it is hard to be sure what you mean. Is it $4 \sqrt {\pi^2+4}$? – Ross Millikan Mar 21 '12 at 20:15
• @Ross Yes he does. – Pedro Tamaroff Mar 23 '12 at 2:32