How do you find the length of an arc in a circle?

Asked on by kazz3014

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

To calculate the length of an arc in the circle you need to measure the radius (r ), and the central angle (a)

The central angle is the angle subtended at the center of a circle by two given points on the circle.

or, the central angle is the ratio of the arc to the radius.

The length of the arc = radius X central angle

                  or s= r * a

Example: in a circle whose radius is 10 cm, and the central angle is 4/5 ... find the length of the arc

    s = r * a = 10 * 4/5 = 8 cm

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The arc of a circle is any connected part of the circumference of the circle. Please note that the term 'arch' should not be confused with arc. Arch refers to a part in a any building or any other structure that supports weight above. Arches are used in structures to make openings in walls for doors and windows and to support other structures like roofs.

The length of an arc can be calculated from the the measure of the central angle subtended by it. Thus:

Length of arc = (Radius of circle)x(Central angle in radians)

If the angle is measured in degrees the formula becomes:

Length of arc = (Radius of circle)x(Central angle in degrees)x(2pi/360)

Please note that value of pi is approximately equal to 22/7

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The length of arch between any two points of any circle depepends upon (i) the radius of the circle and(ii) the angle the arch subtends at the centre of the circle.

If A and B are any two points on a circle of radius r and centre O of the circle and the arch AB subtends an angle AOB , then arch length of AB along the circumference of the circle is  given by:

Arch length AB = r *angle AOB, if the angle AOB is in radian measure = (2pi*r )* angle AOB in degrees/360.



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