Calculate the radius for the section of a circle

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A section of a circle can be imagined as a piece of cake that has been cut out of a round cake. Would you like to calculate the radius of the associated circle? There are various ways of doing this, depending on the sizes.

This indicates a section of a circle

The section of a circle, also known as a sector of a circle, is part of a circular area.

  • It is bounded by two circular radii, which extend from the center point to the circular line, and the circular arc enclosed by it.
  • The section of a circle is characterized by its area, the radius of the circle, the length of the The circular arc and the central angle formed by the two associated circular radii in the center of the circle will. If two of these quantities are given, the other two can be calculated.
  • Do not confuse the segment of a circle with the segment of a circle, which is also known as a segment of a circle. This is limited by a chord and the associated arc.

Determine the radius with a known area and arc

  1. Multiply the area by 2.
    2. Calculate the diameter - this is how it works

    To calculate a circle it is also necessary to be able to calculate the diameter. Depending on, …

  2. Divide the result by the arc length.

Example: If the area is 12.57 cm2 and the arc length is 4.19 cm, you get an associated radius of 6 cm.

Calculate the size for a given arc and central angle

  1. Multiply the arc length by 360 degrees.
  2. Divide the result by 2π.
  3. Divide this amount by the size of the central angle.
  4. Round the result sensibly, because by using π in the formula you will get some decimal places.

Example: A central angle of 40 degrees and a circular arc length of 4.19 cm results in a radius of 6 cm.

When the area and central angle are known

  1. Multiply the area by 360 degrees.
  2. Divide the result by the size of the central angle.
  3. Divide the amount received by π.
  4. Take the square root of this result.
  5. Round off the result sensibly.

Example: With a central angle of 40 degrees and an area of ​​12.57 cm2 again calculate a radius of 6 cm.

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