Answered

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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?

The Radius Of Circle O Not Shown Is 4 And The Radian Measure Of Central Angle AOB Is Between 3pi4 And 5pi4 Which Could Be The Length Of Arc AB class=

Sagot :

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

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