Question

Select the correct answer. What is the length of the indicated arc ?

A. 2π
B. 4π
C. 9π
D. 18π
E. None of the above

Answer 1

Convert theta to radians

• 40°
• 40π/180
• 2π/9

Now

`\\ \rm\rightarrowtail L=r\theta`

`\\ \rm\rightarrowtail L=18(2\pi/9)`

`\\ \rm\rightarrowtail L=4\pi`

Option B is correct

Answer 2

B.
`4\pi`

Explanation:

`\mathsf{arc \ length=(2\pi r\theta)/(360)}`

(where
`\theta` is the angle of the sector measured in degrees and r is the radius)

`\implies \mathsf{arc \ length=(2\pi \cdot 18 \cdot 40)/(360)=(1440\pi)/(360)=4\pi}`