Question

A farmer is putting up a fence for her animals. She orginally had the fence enclosing a square was 18ft by 18ft. Suppose she uses the same amount of fencing to enclose a circular area. What is the area of the circle?

Answer 1

First look: More than 324 square feet :)
Now,
`l=2\pi*r` which means that
`r=(l)/(2\pi)`. But l is the original perimeter, 4 times the side of the square, that is, 72 ft. So,
`r=(72)/(2\pi)=(36)/(\pi)`
Now, the area of that circle is
`A=\pi*r^2=\pi*(1296)/(\pi^2)=(1296)/(\pi)`, which is about 412.5 square feet. It's true, that's more (that's the most you can actually get with that amount of fence :) )