Answer:
Second option is correct
[tex]Arc\ length = \frac{3}{4} \pi\ in[/tex]
Step-by-step explanation:
Given:
Central angle = 15°
Radius of the circle = 9 in
Arc length = ?
Given formula is
[tex]\frac{Arc\ length}{Circumfrance} = \frac{n}{360}[/tex]
Where n is the central angle of the sector.
Write the given formula for Arc length of the sector.
[tex]Arc\ length = Circumfrance\times \frac{n}{360}[/tex]
We know that the the circumference of the circle is [tex]2\pi r[/tex], where r is the radius of the circle,
[tex]Arc\ length = 2\pi r\times \frac{n}{360}[/tex]
Now we substitute central angle value and radius value in above equation.
[tex]Arc\ length = 2\pi 9\times \frac{15}{360}[/tex]
[tex]Arc\ length = 18\times \pi \frac{15}{360}[/tex]
[tex]Arc\ length = \frac{18\times 15}{360} \pi[/tex] ----------([tex]\frac{18}{360}=\frac{1}{20}[/tex])
[tex]Arc\ length = \frac{15}{20} \pi[/tex]
Divide the numerator and denominator by 5.
[tex]Arc\ length = \frac{3}{4} \pi\ in[/tex]
Therefore the arc length of the sector is [tex]\frac{3}{4} \pi\ in[/tex]
