Question

The radius of circle O (not shown) is 4, and the radian measure of central angle AOB is between 3pi/4 and 5pi/4. which could be the length of arc AB?

Answer 1

Write out the formula for the length of an arc

`\begin{gathered} \text{length of Arc=}\theta* r \\ \text{Where }\theta\text{ is in radians } \\ r=4 \end{gathered}`

Angle given is between

`(3\pi)/(4)\text{ and }\frac{\text{5}\pi}{4}`

Substitute each of the value for Θ in the formula above

`\begin{gathered} \text{When }\theta=(3\pi)/(4) \\ \text{Then} \\ \text{Length of Arc=}\theta* r=(3\pi)/(4)*4=3\pi \end{gathered}`

Also

`\begin{gathered} \text{when }\theta=(5\pi)/(4) \\ \text{Then} \\ \text{Length of Arc=}(5\pi)/(4)*4=5\pi \end{gathered}`

Hence

The length of the Arc is between

`\begin{gathered} 5\pi\text{ } \\ \text{and } \\ 3\pi \end{gathered}`

Therefore

The length of the Arc AB could be 4π

Answer :Option B