Math CentralQuandaries & Queries


Question from lachlan, a student:

A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m.

a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %?

b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be?


For a I got ratio of the area that the goat can graze to the area of the paddock to be π/16 which is 19.63%.

Since our answers agree in part a I expect we made the same calculation. You can use the same idea for part b. This time you don't know the length of the rope so call it r m. The region that the goat can graze is then a quarter circle of radius r. Write an expression for the area of one quarter of a circle of radius r and set it equal to one half the area of the paddock. Solve this for r.


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