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.
The answer is C, I looked at his answer and all that is different is he multiplied the equation in the parentheses by 2!!!
answer choices
38TTx^2
22x^2(27-2TT)
2x^2(27-8TT)
38x^2
(6x)(9x)-π(4x)^2 = 54x^2-16πx^2 = (54-16π)x^2
or about 3.73x^2
thank u ella!
To find out how much land will be left over after the jungle gym is built, we need to calculate the area of the entire rectangular lot and subtract the area of the circular jungle gym.
1. Calculate the area of the rectangular lot:
The rectangular lot measures 6x by 9x, so the area A_rectangular is given by: A_rectangular = length x width.
A_rectangular = 6x * 9x = 54x^2.
2. Calculate the area of the circular jungle gym:
The area of a circle is given by the formula: A_circle = π * r^2, where π (pi) is a constant approximately equal to 3.14 and r is the radius of the circle.
In this case, the radius r of the circular jungle gym is given as 4x. So, A_circle = 3.14 * (4x)^2 = 3.14 * 16x^2 = 50.24x^2.
3. Find the remaining area after the jungle gym is built:
To calculate the remaining area, subtract the area of the circular jungle gym from the area of the rectangular lot.
Remaining Area = A_rectangular - A_circle = 54x^2 - 50.24x^2 = 3.76x^2.
Therefore, the remaining land after building the jungle gym will be 3.76x^2.