There is a circular garden in the middle of a square yard. The radius 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?
well, what is
(20x)^2 - pi(4x)^2 ?
I am fairly sure the answer would be represented by the following polynomial:
-pi(24x)^2
But if anyone else comes up with something they're completely sure is correct, go with that answer instead.
123111
To find the area of the part of the yard that is not covered by the circle, we need to find the area of the square yard and subtract the area of the circular garden.
1. Area of the square yard:
The side length of the square yard is given as 20x. To find the area of a square, we square the length of one side.
Area of the square yard = (20x)^2 = 400x^2
2. Area of the circular garden:
The radius of the circular garden is given as 4x. We can use the formula for the area of a circle, which is πr^2, where π is a mathematical constant approximately equal to 3.14159.
Area of the circular garden = π(4x)^2 = 16πx^2
3. Calculate the area of the part of the yard that is 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.