ARC LENGTH OF A CIRCLE
Definition Of Arc Length Of A Circle
Length of an Arc is the fractional part of the circumference subtended by the arc in a circle.
More About Arc Length of a Circle
Length of arc = 
× Π × d, where d is the diameter of the circle.
Examples of Arc Length of a Circle
In the above circle, the distance between A and B is the length of an arc
Video Examples: Finding Arc Length of a Circle
Solved Example Clockple on Approximate
Ques: The circumference of a circle is 40 Π cm. Find the length of an arc whose measure is 540
Choices:
A. 6Π cm
B. 5Π
C. 12Πcm
D. 40Π cm
Correct Answer: A
Solution:
Step 1: Circumference = 40Π [Given.]
Step 2: d = 40 cm [Circumference = Πd.]
Step 3: Length of arc = × Π × d [Formula for the length of an arc of a circle.]
Step 4: Length of arc = 
× Π × 40 [Substitute the given values.]
Step 5: Length of arc = 6Π cm [Simplify.]
Quick Summary
- Arc length is a portion of a circle's circumference.
- Arc length can be calculated using the formula: Arc Length = (central angle/360) * 2 * pi * radius.
- If the central angle is in radians, Arc Length = radius * central angle.
🍎 Teacher Insights
Use visual aids and real-world examples like slices of pizza or curved roads to illustrate arc length. Emphasize the importance of using radians in the formula s=rθ. Provide ample practice problems with varying levels of difficulty.🎓 Prerequisites
- Circumference of a circle
- Diameter of a circle
- Radians and degrees
Check Your Knowledge
Q1: A circle has a radius of 10 cm. What is the arc length subtended by a central angle of 90 degrees?
Q2: A circle has a diameter of 20 cm. What is the arc length subtended by a central angle of π/3 radians?
Frequently Asked Questions
Q: How do you convert degrees to radians?
A: Multiply the degree measure by π/180.
Q: What is the relationship between arc length and circumference?
A: Arc length is a fraction of the total circumference, determined by the central angle.