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 r^2
A = 2r^2 – pi r^2
A = 4r^2 –pi r^2
A = 4r^2 – pi r^2
The correct rule for the area A of grass as a function of r is:
A = 4r^2 - πr^2
To find the rule for the area of grass as a function of r, we need to determine the area inside the square but outside the circle.
First, let's calculate the area of the square. The side length of the square is 2r, so the area of the square is (2r)^2 = 4r^2.
Next, let's calculate the area of the circle. The formula for the area of a circle is A = πr^2, where π is a constant approximately equal to 3.14159. Therefore, the area of the circle is πr^2.
To find the shaded area, we subtract the area of the circle from the area of the square: 4r^2 - πr^2.
Therefore, the rule for the area A of grass as a function of r is A = 4r^2 - πr^2, which is option D.