Formulas for Arc Length
The formula to measure the length of the arc is –
|Formula for arc length (if θ is in degrees)||s = 2 π r (θ/360°)|
|Formula for arc length (if θ is in radians)||s = ϴ × r|
|Formula for arc length in Integral Form||s= ∫ba1+(dydx)2−−−−−−−−√dx|
Denotations in the Arc for Length Formula
- s is the arc length
- r is the radius of the circle
- θ is the central angle of the arc
Question 1: Calculate the length of an arc if the radius of an arc is 8 cm and the central angle is 40°.
Radius, r = 8 cm
Central angle, θ = 40°
Arc length = 2 π r × (θ/360°)
So, s = 2 × π × 8 × (40°/360°)
= 5.582 cm
Question 2: What is the arc length for a function f(x) = 6 between x = 4 and x = 6?
Since the function is a constant, the differential of it will be 0. So, the arc length will now be-
s=∫641+(0)2−−−−−−−√dxSo, arc length (s) = (6 – 4) = 2.
Practice Questions Based on Arc of length Formula
- What would be the length of the arc formed by 75° of a circle having the diameter of 18 cm?
- The length of an arc formed by 60° of a circle of radius “r” is 8.37 cm. Find the radius (r) of that circle.
- Calculate the perimeter of a semicircle of radius 1. cm using the arc length formula.