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Equations for Finding the Perimeter & Sector of a Circle

The perimeter of a circle is the distance around the outside of the circle. You can find the perimeter if you know or can measure the diameter, which is the distance across the center of the circle. The sector of a circle is a wedge of the circle, similar to a slice of pie. You can find the area of a sector of a circle if you know, or can measure, the diameter and the angle of the sector.
  1. Pi

    • Problems involving circles quite often involve the number pi (the Greek letter). This is defined as the ratio of the circumference (or perimeter) of a circle to its diameter. Although good approximations were known in ancient times, there is no exact value for pi. This was proved by Johann Lambert in 1761. Pi is now known to billions of digits, but such precision is not needed. In fact, that many digits would allow you to find the area of a circle the size of the galaxy to the accuracy of the size of an atom.

    The Perimeter of a Circle

    • The perimeter is a geometric term for the area around any shape, whether it is a square, a hexagon, an irregular shape or a circle. Another term for the perimeter of a circle is circumference. The formula for finding the circumference of a circle is pi x d, where d is the diameter. For practical purposes, approximating pi as 3.14 is usually enough.

    The Sector a Circle

    • The sector of a circle is a shape made by making two straight lines from the center to the edge of a circle. Sectors with relatively small angles are wedge-shaped, like pieces of pie. The formula for finding the area of a sector is arc x pi x r^2 / 360. To find the area of a sector, multiply the angle (measured in degrees) by pi. Then multiply the result by the radius squared (the radius is half the diameter), then divide by 360.

    Examples of the Formulas

    • A circle that is 2 feet across has an perimeter of about 6.28 feet, because 2 x 3.14 = 6.28.

      A sector of a circle that is 3 feet across and with an angle of 90 degrees has an area of approximately 90 x 3.14 x 1.5^2 / 360 = 635.85 / 360 = 1.77 square feet. Remember that area must be in squared units of length (here, it is square feet).

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