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?
circle has area pi * (4x)^2 = 16pi x^2
yard has area (20x)(20x) = 400x^2
so, subtract circle from yard to get ...
To find the area of the part of the yard that is not covered by the circle, we need to subtract the area of the circle from the area of the square yard.
First, let's determine the area of the square yard. The side length of the square yard is given as 20x, so we can find the area by squaring the side length:
Area of the yard = (side length)^2 = (20x)^2 = 400x^2
Next, let's find the area of the circle. The radius of the circle is given as 4x, so we can use the formula for the area of a circle:
Area of the circle = π * (radius)^2 = π * (4x)^2 = 16πx^2
Now, we can subtract the area of the circle from the area of the yard to find the area of the part that is not covered by the circle:
Area not covered by the circle = Area of the yard - Area of the circle
= 400x^2 - 16πx^2
Therefore, the area of the part of the yard that is not covered by the circle is 400x^2 - 16πx^2.