SOLUTION
Write out the formula for the length of an arc
[tex]\begin{gathered} \text{length of Arc=}\theta\times r \\ \text{Where }\theta\text{ is in radians } \\ r=4 \end{gathered}[/tex]
Angle given is between
[tex]\frac{3\pi}{4}\text{ and }\frac{\text{5}\pi}{4}[/tex]
Substitute each of the value for Θ in the formula above
[tex]\begin{gathered} \text{When }\theta=\frac{3\pi}{4} \\ \text{Then} \\ \text{Length of Arc=}\theta\times r=\frac{3\pi}{4}\times4=3\pi \end{gathered}[/tex]
Also
[tex]\begin{gathered} \text{when }\theta=\frac{5\pi}{4} \\ \text{Then} \\ \text{Length of Arc=}\frac{5\pi}{4}\times4=5\pi \end{gathered}[/tex]
Hence
The length of the Arc is between
[tex]\begin{gathered} 5\pi\text{ } \\ \text{and } \\ 3\pi \end{gathered}[/tex]
Therefore
The length of the Arc AB could be 4π
Answer :Option B
