A garden will be on a rectangle lot 5x by 10x. The garden will be circular with a radius of 3x. How much land will be left over after the garden is built?
To find out how much land will be left over after the garden is built, we need to calculate the area of the rectangular lot and subtract the area of the circular garden from it.
The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the rectangular lot is 5x and the width is 10x. So the area of the rectangular lot is:
Area of rectangle = Length x Width = 5x * 10x = 50x^2.
The area of a circle can be found using the formula: π * r^2, where π is approximately 3.14159 and r is the radius of the circle. In this case, the radius of the circular garden is 3x. So the area of the circular garden is:
Area of circle = π * (radius)^2 = 3.14159 * (3x)^2 = 28.27433x^2.
Now, we can find the land left over by subtracting the area of the circular garden from the area of the rectangular lot:
Land left over = Area of rectangle - Area of circle = 50x^2 - 28.27433x^2 = 21.72567x^2.
Therefore, the amount of land that will be left over after the garden is built is 21.72567x^2.