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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?
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.
Step 1: Area of a circle
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
In this case, the radius of the circle is 4x. Therefore, the area of the circle is A = π(4x)^2.
Simplifying this, we get A = 16πx^2.
Step 2: Area of the square yard
The formula to find the area of a square is A = s^2, where A is the area and s is the side length.
In this case, the side length of the yard is 20x. Therefore, the area of the square yard is A = (20x)^2.
Simplifying this, we get A = 400x^2.
Step 3: Area not covered by the circle
To find the area not covered by the circle, we subtract the area of the circle from the area of the square yard.
A = Area of square yard - Area of circle
A = 400x^2 - 16πx^2
Simplifying, we get A = (400 - 16π)x^2.
So, the area of the part of the yard that is not covered by the circle is (400 - 16π)x^2.
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.
1. Area of the circle:
The formula to calculate the area of a circle is A = π * (radius)^2.
In this case, the radius of the circle is 4x, so the area of the circle is A_c = π * (4x)^2 = 16πx^2.
2. Area of the square yard:
The formula to calculate the area of a square is A = (side length)^2.
In this case, the side length of the square yard is 20x, so the area of the square yard is A_y = (20x)^2 = 400x^2.
3. Calculate the area of the part of the yard not covered by the circle:
To find this area, we subtract the area of the circle from the area of the yard:
A_not_covered = A_y - A_c = 400x^2 - 16πx^2.
So the area of the part of the yard that is not covered by the circle is 400x^2 - 16πx^2 square units.