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 20. 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)***

Your answer is right, but you should have typed the problem correctly.

Assuming the circle reaches the edge of the square ....

area of square = 400
area of circle = 16pix^2

area not covered by circle
= 400 - 16pix^2
= 16( - pix^2)

none of the answers given match

To find the area of the part of the yard that is not covered by the circle, we first need to calculate the area of the circle and subtract it from the total area of the square yard.

The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.

In this case, the radius of the circle is given as 4x. Plugging the value into the formula, we have A = π(4x)^2.

Simplifying further, we have A = π * 16x^2, which equals 16πx^2.

The area of the square yard is given as 20 times 20, which is 400.

To find the area of the part of the yard that is not covered by the circle, we subtract the area of the circle from the total area of the square yard: 400 - 16πx^2.

Looking at the available answer choices, we can see that option d. 16x^2(25-pi) matches the expression we obtained, 400 - 16πx^2.

Therefore, the correct answer is d. 16x^2(25-pi).