You have a choice of climbing on of three geometrically shaped mountains, which are all 10000 feet high. One of the mountains is a perfect cylinder, another  is in the shape of a cone, and the third looks like the top half of a sphere. Several out of the math work teachers have constructed roads that go from the base to the summit(top) of each mountain. All three roads are built so that you climb 1 vertical foot every 20 horizontal feet. If you wish to walk the shortest distance from base to summit, which would you choose?