As a graduation prank, several Sherando students decided to paint the Handley Smokestack to make it look like a candy cane stick (like a candy cane but without the curl). The Smokestack is a cylinder, 110 feet tall and 20 feet in diameter. The pranksters are going to paint the smokestack white and have a single red stripe that winds exactly 12 times around from top to bottom as shown in the diagram below.

One of the students volunteers to buy the red stripe. How long a stripe does he need? Round off your answer to the nearest foot.

Picture of smokestack
Click here for a picture of the real Handley Smokestack by Scott Mason

 

Solution to the Problem:

The answer is 762 feet.
Unrolled, the candy cane stick forms a rectangle with the stripe crossing it diagonally, as in the diagram below.

unrolled cylinder

formula

Correctly solved by:

1. Keith Mealy Cincinnati, Ohio
2. David & Judy Dixon Bennettsville, South Carolina
3. Walt Arrison Philadelphia, Pennsylvania
4. Jim Arrison Norristown, Pennsylvania
5. James Alarie University of Michigan -- Flint,
Flint, Michigan
6. Tom Robb Winchester, Virginia
7. António Baptista Lisboa, Portugal
8. Angelo Leone Middletown, Connecticut
9. Trey Mason Winchester, Virginia
10. Viktor Logrell, Jonathan Jansson, Bahadér Güngör, Ako Saleh Tullängensskolan, Örebro, Sweden
11. Tristan Collins Winchester, Virginia
12. Jeffrey Gaither Winchester, Virginia
13. Daniel Surber Winchester, Virginia
14. Gwen Conis Harrisonburg, Virginia
15. Cameron Burkholder Winchester, Virginia
16. Daniel Gardiner Winchester, Virginia
17. Mike Singer Winchester, Virginia
18. Camila Domonoske Harrisonburg, Virginia
18. Mikael Wetterholm Royal Institute of Technology,
Stockholm, Sweden
19. Ben Swartz Winchester, Virginia
20. Wajih Ansari Harrisonburg Virginia
21. Chris Rogers Winchester, Virginia
22. Arsalan Heydarian Harrisonburg Virginia
23. Hamza Rashid Harrisonburg Virginia
24. Kenneth Link Winchester, Virginia