Content

• To step
• Method 1 of 4: Area of ​​a circle
• Method 3 of 4: Special circles
• Method 4 of 4: Measure the diameter of round physical objects
• Tips
• Warnings
• Necessities

Follow these steps to calculate the area of ​​a circle. You will also learn how to calculate the area of ​​a sector, which is the slice of a pie of a circle, such as the shape of a slice of pizza or pie.

To step

Method 1 of 4: Area of ​​a circle

1. Calculate the size of the slice in degrees. Unfortunately, there is no set way to do this. The result will vary significantly depending on what information is provided in the problem. And it is not possible to include a step-by-step process for every situation.
2. Calculate the radius of a circle. Again, the radius is exactly half the diameter.
3. Calculate the area of ​​the circle. See the section above for a description of how to do this.
4. Make a break. Your fracture should have:
   • The counter in the form of the angle (in degrees) of the slice, and
   • 360 ° as the denominator.
5. Simplify the fraction. Divide the numerator and denominator by their greatest common divisor to simplify your fraction.
6. Multiply this fraction by the area of ​​the circle and you're done!
   • Alternatively (instead of simplifying the fraction) you can multiply the area by the number of degrees in the slice, then divide by 360 °.
7. Here's an example:
   • The exact result with pi:
   • Approximation with the decimal:
   • Usually you will not get an integer coefficient for pi. However, if your radius is a multiple of three, then you will get some sort of division between the fraction and the result of the (). You will have to decide to: (a) keep the fraction as the fraction and pi as the pi symbol, and cross out as much as possible, or (b) replace with 3.14 and complete the division completely.

Method 3 of 4: Special circles

1. Know what to do in these special cases:
   • Sometimes you will come across a "circle within a square". The side length of this square is equal to the "diameter of the circle.
   • You also sometimes see a "square in a circle". The length of the diagonal of this square is equal to the diameter of the circle!

Method 4 of 4: Measure the diameter of round physical objects

1. Use a flexible "tape measure", such as is used in sewing, to measure the outside of the object. Measure this in centimeters. This will give you the circumference. Divide by 3.14 to estimate the diameter.
2. If you don't have a flexible tape measure, use a piece of string to measure the circumference of the object. Then measure this length with a ruler and divide by 3.14 to find out the approximate diameter.
3. With a cylindrical object, such as a soup can, you can place a ruler on top of the can. Hold one end while twisting the other end. Keep turning until you get to the point with the longest distance. This is the diameter
4. Use a caliper to measure the object.

Tips

• Remember you have to square the radius, not the diameter.
• Note that 3.14 is an approximation of Pi only; there are actually an infinite number of decimal places. In such cases, use a calculator for a more accurate calculation.
• Try to remember the formula during exams.
• If you can't find help anywhere else, ask a friend or family member, search the Internet, or check a math textbook.
• It is helpful if you have a calculator handy. A simple 4 calculator is sufficient, but more advanced calculators can save your measurements for later use. Or you can also use the calculator on your computer.
• Write everything on a notebook.

Warnings

• It's hard to be accurate with measurements when you're working on a large scale. Keep this in mind when you start calculating and measuring.
• While forming a triangle around a rounded edge is a quick way to approximate the area of ​​a slice of pie, it is not the most precise way, especially with larger circles.

Necessities

• Pencil
• Paper
• Ruler (to measure diameter) or flexible tape measure (to measure circumference)
• Calculator