cutting a circle into equal sections of a small central angle to find the area of a circle by using formulae

To cut a circle into equal sections of a small central angle, you can use a common technique known as radial lines or radii. Here's how you can do it:

1. Start by drawing a circle using a compass or any circular object. This will be your reference circle.

2. Choose a point on the circumference of the circle. This point will be the center of the small central angle.

3. Using a protractor, measure the desired central angle. Let's say you want to divide the circle into n equal sections, each with a central angle α.

4. Divide the total angle of a circle (which is 360 degrees or 2π radians) by the number of sections (n) to determine the value of α. So, α = (360 degrees)/n or α = (2π radians)/n.

5. Using a ruler, draw radial lines from the center of the circle to the edge, making sure each line forms an angle of α with the adjacent line. Continue drawing these lines until the entire circle is divided into n equal sections.

Now, onto finding the area of the circle using a formula:

The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.

To calculate the radius, you need to know either the diameter or the circumference of the circle. If you know the diameter (d), divide it by 2 to get the radius (r). If you know the circumference (C), divide it by 2π to get the radius (r).

Once you have the radius, substitute its value into the formula A = πr^2 and calculate the area of each section using the small central angle (α) as a fraction of the entire circle.

To find the area of each section, multiply the area of the entire circle by α divided by 360 degrees (or 2π radians).

So, the area of each section would be (πr^2) * (α/360) or (πr^2) * (α/(2π)).

In summary, divide the circle into equal sections of a small central angle using radial lines, and then use the formula A = πr^2 to find the area of the entire circle. Finally, calculate the area of each section by multiplying the area of the entire circle by α divided by 360 degrees (or α divided by 2π radians).

you have the formula, right?

So plug in your numbers.

Don't no