A community group is building a playground on a rectangular lot of land. The lot measures 6x by 9x and they want to cut out an area for a circular jungle gym with a radius of 4x. How much of the land will be left over after the jungle gym is built?
To find out how much land will be left over after the jungle gym is built, we first need to find the area of the rectangular lot and the area of the circular jungle gym.
1. Area of the rectangular lot:
The length of the rectangular lot is given as 6x, and the width is given as 9x.
The area of a rectangle is calculated by multiplying the length by the width.
So, the area of the rectangular lot = 6x * 9x = 54x^2.
2. Area of the circular jungle gym:
The radius of the circular jungle gym is given as 4x.
The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
So, the area of the circular jungle gym = π * (4x)^2 = 16πx^2.
3. Subtracting the area of the circular jungle gym from the area of the rectangular lot will give us the remaining land area.
Remaining land area = Area of the rectangular lot - Area of the circular jungle gym
Remaining land area = 54x^2 - 16πx^2.
Therefore, the amount of land that will be left over after building the jungle gym is 54x^2 - 16πx^2.
To find out how much land will be left over after the jungle gym is built, we need to calculate the area of the rectangular lot and subtract the area of the circular jungle gym.
1. Calculate the area of the rectangular lot:
The area of a rectangle is given by the formula: Area = length × width.
In this case, the length of the rectangle is 6x and the width is 9x.
So, Area of the lot = 6x × 9x = 54x^2.
2. Calculate the area of the circular jungle gym:
The area of a circle is given by the formula: Area = π × radius^2.
In this case, the radius of the circle is 4x.
So, Area of the jungle gym = π × (4x)^2 = 16πx^2.
3. Subtract the area of the jungle gym from the area of the lot:
Land left over = Area of the lot - Area of the jungle gym
Land left over = 54x^2 - 16πx^2
Thus, the amount of land left over after the jungle gym is built is 54x^2 - 16πx^2.