Sheep on a hill
There is a hemispherical hill of radius R on which 4 sheep graze. Each sheep has its own area to graze, which is created by fencing distances horizontally (along latitudes) at equal vertical distances. The top area is given to sheep 1,and lower ones to sheep 2, 3 and 4.Which sheep will have the most grass to eat?
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1 solution
Area of a cap is S c a p = 2 π R h
There are four caps with h = R , 4 3 R , 2 R , 4 R
Since the areas are proportional to h an h increases in equal steps, the areas accessible to the sheep which are the differences between successive caps are all equal.