How do you find the arc length of a circle? If possible provide an example.
Answers
Answer:
A circle is 360° all the way around; therefore, if you divide an arc's degree measure by 360°, you find the fraction of the circle's circumference that the arc makes up. Then, if you multiply the length all the way around the circle (the circle's circumference) by that fraction, you get the length along the arc.
Formula:-
2Arc length = 2πr (θ/360)
θ = the angle (in degrees) subtended by an arc at the center of the circle. 360 = the angle of one complete rotation. From the above illustration, the length of the arc (drawn in red) is the distance from point A to point B.
ANSWER
● What is an Arc of a Circle?
An arc of a circle is any portion of the circumference of a circle.
● How to Find the Length of an Arc?
The formula for calculating the arc states that:
Arc length = 2πr (θ/360)
Where r = the radius of the circle
Example :-
Given that arc, AB subtends an angle of 40 degrees to the center of a circle whose radius is 7 cm. Calculate the length of arc AB.
Solution :
=> Given r = 7 cm
=> θ = 40 degrees.
By substitution,
=> The length of an arc = 2πr(θ/360)
=> Length = 2 x (22/ 7)x 7 x 40/360
= 44/ 9 cm
OR
= 4.884 cm.
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Hope this helps!
