Fly and Spider

by

Teisha, Angie, and Beth


A room has the shape of a right circular cylinder with radius r = 10ft abnd height h = 8ft. A spider is on the room's ceiling , 7 feet from and directly to the east of the ceiling's center. A fly on the room's floor, 7 feet from and directly to the west of the floor's center. Determine (analytically or numerically) the minimum distance the spider would have tyo crawl in order to reach the fly.


An analytic solution:
First, it is easiest to first get a picture of the problem and the solution becomes easier to see. From the picture we can see that the spider is sitting along a radius of the circular ceiling and the fly is sitting along a radius of the cicular floor.

If the fly is 7 feet from the center then he is only 3 feet from the edge of the floor and similarly the spider is only 3 feet from the edge of the ceiling. Now if we can determine the shortest route for the spider to travel around the cylinder we will have the problem solved.
To do this we look at the surface area of the cyllinder. The surface area of a circular cylinder is simply a rectangular region with height of 8 and width equal to the cicumference of the ceiling.

The shortest distance from the east side of the ceiling to the west side of the floor is the line that follows the path of the diagonal of the rectangular region. Therefore, if the spider travels the path along the radius to the edge, then follows the path of the diagonal of the region, and simply follows the path of the radius that the fly is sitting on , it will have crawled the shortest possible distance.


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