Pre-Calculus Function

Question

A piece of rope that is feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Write a function representing the area of the circle as a function of the length of one side of the square 

Hint: If is the circumference of the circle and is the perimeter of the square, then 

Enter the expression in simplest form.

f(s) =

Answer 1

Circumference = piD = 2pir = R-4s where R=rope length and r = the circle's radius

r = (R-4s)/2pi

pir = (R-4s)/2

Area = pir(r) = (R-4s)^2/4pi

Area = f(s) =(1/pi) ((R-4s)/2)^2

or

f(s) = R^2/4pi - 2R/pi + 4/pi