What is the length of an arc cut off by an angle of 2.75 radians on a circle of radius 4 inches?

Question

What is the length of an arc cut off by an angle of 2.75 radians on a circle of radius 4 inches?

Answer 1

The formula for the length of an arc is:

L=(πd)*(angle/2π)    or     L=(2πr)*(angle/2π)

 

We are given radius, so let's use the second version.

L = (2*π*4)*(2.75/2π)

L = 22π/2π

L = 11

Answer 2

s = θ*r

 

Where:

s = arc length

θ = the angle subtending the arc, measured in radians = 2.75 radians

r = radius of the circle = 4 inches

 

s = (2.75)*4 = 11 inches