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

SOLUTION

Write out the formula for the length of an arc

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

Angle given is between

$\frac{3\pi}{4}\text{ and }\frac{\text{5}\pi}{4}$

Substitute each of the value for Θ in the formula above

$\begin{gathered} \text{When }\theta=\frac{3\pi}{4} \\ \text{Then} \\ \text{Length of Arc=}\theta\times r=\frac{3\pi}{4}\times4=3\pi \end{gathered}$

Also

$\begin{gathered} \text{when }\theta=\frac{5\pi}{4} \\ \text{Then} \\ \text{Length of Arc=}\frac{5\pi}{4}\times4=5\pi \end{gathered}$

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