Math CentralQuandaries & Queries


Question from Dave:

I'm buying a wireless fence to keep my pet in my yard. It has a half acre range. In a straight line how far would that be?

Hi Dave,

There are different types of wireless fences but I think the one you are considering has a central transmitter that gives your pet a circular safe region that has an area of one half an acre. One acre is 43560 square feet and the area of a circle is $\pi \; r^2$ square feet where $r$ is the radius in feet and $\pi$ is approximately 3.1416. Thus you have

\[\pi \; r^2 = \frac{43560}{2} = 21780\]


\[r = \sqrt{ \left( \frac{21780}{\pi} \right)} = 83 \mbox{ feet.}\]

I hope this helps,

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