Question

A piece of rope that is 26feet 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 g representing the area of the square as a function of the radius of the circle r.

Answer 1

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Answer:

  g(r) = (13 -πr)²/4

Step-by-step explanation:

The circumference of the circle is given by ...

  C = 2πr

The amount of rope remaining after the circle is formed will be ...

  26 -2πr

When this is used to form a square, each side of the square will be 1/4 of this length, so is ...

  s = (26 -2πr)/4 = (13 -πr)/2

The area of the square is the square of the side lengths, so is ...

  g(r) = ((13 -πr)/2)²

  g(r) = (13 -πr)²/4 . . . . area of the square as a function of circle radius