Cutting a circle into equal sections of a small central angle to find the area of a circle by using the formula A=pi*r*r
If you cut the circle into many slices, each slice is approximately an isosceles triangle, with height = r.
Slicing the circle into, say, 2000 wedges, each triangle has a base of almost (2pi*r)/2000 = pi*r/1000
Each triangle has an area = 1/2 bh = 1/2 (pi*r/1000)*r = pi*r^2/2000
Since there are 2000 triangles, the area is pi*r^2
The approximation gets better the more triangles there are.
360/60=6
To find the area of a circle using the formula A = π * r^2 and dividing it into equal sections of a small central angle, you can follow these steps:
1. Start with a circle with a given radius, labeled as r.
2. Divide the circle into equal sections by drawing lines from the center of the circle to the circumference, dividing it into smaller wedges. The central angle of each wedge should be equal.
3. Choose one of the wedges and mark its central angle, denoted as θ. Remember, the total central angle for the whole circle is 360 degrees or 2π radians.
4. Calculate the area of the wedge by using the formula for the area of a sector, A_sector = (θ/2π) * π * r^2. The θ/2π fraction represents the ratio of the angle of the wedge to the total angle of the circle.
5. Since all the wedges have the same central angle, all the sectors will have the same area. Therefore, the area of each wedge is equal to A_sector.
6. To find the area of the entire circle, multiply the area of the wedge (A_sector) by the total number of wedges.
This method allows you to divide the circle into equal sections to estimate the total area by multiplying the area of one wedge by the total number of wedges.