A local farmer wants to keep his sheep safe. He has one mile of fence, with which to surround the sheep. Luckily there is a very straight river which he can also use. Obviously the farmer wants to fence off as much land as possible, what shape will the fenced off area be and how much actual space will it encompass?

A right triangle, with the river forming the hypotenuese, encompassing 1 square mile of land. Each section of fence will be .5 miles in length.

That is not the answer, Jimmy Barcus.

Keep trying.

If I were the farmer, I’d actually make the fenced off area as a semi-circle with the river as a diameter.

That’s correct Anant, but that’s only half the answer?

How much space will it actually encompass?

15.91 Sq. Miles

oops! 0.1591 Sq. Miles

Great job Anant!

The area of the entire circle would be Pi x (1 / Pi) x (1 / Pi) = 1 / Pi.

We only want half of this area, so the answer is 1 / (2 x Pi) = 0.16 of a square mile.

You are today’s winner.