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A designer wants to make a circular fountain inside a square of grass as shown at the right. What is a rule for the area A of the grass as a function if r

A designer wants to make a circular fountain inside a square of grass as shown at the right What is a rule for the area A of the grass as a function if r class=

Respuesta :

Answer:

[tex]A=4r^{2}-r^{2}\pi[/tex]


Step-by-step explanation:

1. To calculate the area of the grass you must substract the area of the square and the area of the circle.

2. The area of the square is:

[tex]A1=L^2[/tex]

Where [tex]L[/tex] is one side of the square.

3. You have that:

[tex]L=2r[/tex]

4. Therefore:

[tex]A1=(2r)^{2} =4r^{2}[/tex]

5. The area of the circle is:

[tex]A2=r^{2}\pi[/tex]

6. The are of the grass is:

[tex]A=4r^{2}-r^{2}\pi[/tex]