Donkey on a Rope

There are two variations to this puzzle. Both puzzles involve calculating the area of grass a donkey can eat when attached to a pole in the centre of a field.

In one version, the pole is square and in the other, the pole is circular.

Here is the first puzzle. A donkey is tethered to a circular pole in a field. If the radius of the pole is 150mm and the length of the rope is 4m, find the area of grass the donkey can eat? (The donkey can’t eat further than the rope end.) This is a tricky puzzle and may take some time to work through.

In the meantime, lets consider the slightly easier puzzle where the post the donkey is tethered to is square. The rope is connected to the middle of one side of the square post. The post is 300 mm wide and the length of rope is 4 meters. What is the area of grass the donkey can eat?

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