Apiece of rope there is 28 feet long is cut into two pieces. one is use to form a circle and others 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

The function g representing the area of the square as a function of the radius of the circle r is given as:

Solution:

Given that,

length of rope = 28 feet

Let "c" be the circumference of circle

Let "p" be the perimeter of square

Therefore,

length of rope = circumference of circle + perimeter of square

c + p = 28 ------- eqn 1

The circumference of circle is given as:

Where, "r" is the radius of circle

Substitute the above circumference in eqn 1

----------- eqn 2

If "a" is the length of each side of square, then the perimeter of sqaure is given as:

p = 4a

Substitute p = 4a in eqn 2

The area of square is given as:

Substitute the value of "a" in above area expression

 ------ eqn 3

We know that,

Therefore eqn 3 becomes,

Let g(r) represent the area of the square as a function of the radius of the circle r, then we get

Thus the function is found

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