A designer wants to make a circular fountain inside a square of grass as shown below. What is a rule for the area A of grass as a function of r?
A circle is shown inscribed in a square. The circle has a radius of r, and the square has a side length of 2 r. The area outside the circle but also inside the square is shaded.
(1 point)
Responses
A = 2pi r^2
A = 3.75pi r62
A = 2r^2 – pi r^2
A = 4r^2 –pi r^2
The correct answer is A = 4r^2 – pi r^2.
This is because the area of the square is equal to the side length squared, which is (2r)² = 4r^2. However, the circle only covers a portion of this square, so we subtract the area of the circle from the area of the square. The area of the circle is given by pi r^2. Therefore, the rule for the area of grass is A = 4r^2 – pi r^2.