There is a circular garden in the middle of a square yard. The radius of the circle is 4x. The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle? (1 point) Responses 4x(5) 4 x (5) 8x2(5 – ) 8 x 2 (5 – Image with alt text: symbol pi ) 16x(25 + ) 16 x (25 + Image with alt text: symbol pi ) 16x2(25 – )
The area of the circular garden is given by the formula A = πr², where r is the radius of the circle. In this case, the radius is 4x, so the area of the circular garden is A = π(4x)² = 16πx².
The area of the square yard is given by the formula A = s², where s is the side length of the square. In this case, the side length is 20x, so the area of the square yard is A = (20x)² = 400x².
To find the area of the part of the yard that is not covered by the circle, we subtract the area of the circular garden from the area of the square yard. So the area of the part of the yard that is not covered by the circle is:
400x² - 16πx²
Therefore, the correct answer is 400x² - 16πx².