Saturday, February 18, 2017

Fun Challenging Problems on Shortest Distance

1. The height, h, of the below cylinder is 10m, and the radius, r, is 5m.  The two labelled points A and B are directly opposite of each other on the top and bottom of the cylinder.  What is the shortest route between A and B while travelling on the surface of the cylinder?

2. The diagram below shows the path that Wilson follows every morning to take water from the river to his farm. Help Wilson minimize the total distance traveled from his house to the farm.  Where should he get water from the river?

3. A bit harder than the other two.
A mountain is in the shape of a perfect cone with height of 100m, and a base radius of 100m.  I walk to the bottom of the mountain and am trying to just get to the other side of the mountain.  If I just walk around the mountain from ground level, the distance would be half the circumference, which would be (1/2) (2 pi radius) = 3.14 x 100 = 314m.  Is there a shorter distance I could walk along?  What is the shortest distance?
(I don't mind climbing mountains) 

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