cutting a circle into equal section of a small central angle to find the area of a circle and olso find area by 4 a sector of rectangle from circle
huh?
Area= pie r2
To find the area of a circle, you can use the formula:
A = πr²
where A is the area and r is the radius of the circle.
To cut a circle into equal sections of a small central angle, you can follow these steps:
1. Decide on the number of sections you want to create. Let's say you want to divide the circle into n equal sections.
2. Draw two radii from the center of the circle to the opposite edges of one of the sections. This creates a sector.
3. Find the measure of the central angle of the sector. Since you want to divide the circle into n equal sections, the central angle of each sector will be 360°/n.
4. Use the formula for the area of a sector to find the area of the entire circle. The formula for the area of a sector is:
A_sector = (θ/360°) * πr²
where θ is the central angle in degrees and r is the radius of the circle.
Since the central angle of each sector is 360°/n, substitute that value into the formula:
A_circle = (360°/n / 360°) * πr²
= (1/n) * πr²
This gives you the area of the entire circle.
5. To find the area of one section, divide the area of the circle by the number of sections:
A_section = A_circle / n
= [(1/n) * πr²] / n
= (1/n²) * πr²
Now, to find the area of a rectangle from a circle, you can follow these steps:
1. Draw a rectangle around the circle, such that the sides of the rectangle are tangent to the circle.
2. The length of the rectangle will be equal to the diameter of the circle (which is 2r), and the width will be equal to the radius of the circle (which is r).
3. Use the formula for the area of a rectangle to find the area:
A_rectangle = length * width
= (2r) * r
= 2r²
So, the area of the rectangle formed from a circle is 2 times the square of the radius (2r²).