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? Responses A = 2r2 A = 2 Image with alt text: pi r 2 A = 3.75r2 A = 3.75 Image with alt text: pi r 2 A = 2r2 – r2 A = 2 r 2 – Image with alt text: pi r 2 A = 4r2 –r2
1 answer
The correct response is A = 4r2 – r2. The area of the grass is the area of the whole square minus the area of the circular fountain. The area of the whole square is (2r)2 = 4r2, and the area of the circular fountain is πr2. Therefore, the rule for the area of grass is A = 4r2 – r2.