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?
A. 4x(5)
B. 8x^2(5-pi)
C. 16x(25+pi)
D. 16x^2(25-pi)
The area of the square yard is given by (20x)^2 = 400x^2.
The area of the circular garden is given by π(4x)^2 = 16πx^2.
The area of the part of the yard that is not covered by the circle is therefore 400x^2 - 16πx^2.
Factoring out x^2, we have x^2(400 - 16π).
The correct answer is D. 16x^2(25 - π).