Question

Please help! :)

Answer 1

Answer:

Second option is correct

$Arc\ length = \frac{3}{4} \pi\ in$

Step-by-step explanation:

Given:

Central angle = 15°

Radius of the circle = 9 in

Arc length = ?

Given formula is

$\frac{Arc\ length}{Circumfrance} = \frac{n}{360}$

Where n is the central angle of the sector.

Write the given formula for Arc length of the sector.

$Arc\ length = Circumfrance\times \frac{n}{360}$

We know that the the circumference of the circle is $2\pi r$, where r is the radius of the circle,

$Arc\ length = 2\pi r\times \frac{n}{360}$

Now we substitute central angle value and radius value in above equation.

$Arc\ length = 2\pi 9\times \frac{15}{360}$

$Arc\ length = 18\times \pi \frac{15}{360}$

$Arc\ length = \frac{18\times 15}{360} \pi$               ----------($\frac{18}{360}=\frac{1}{20}$)

$Arc\ length = \frac{15}{20} \pi$

Divide the numerator and denominator by 5.

$Arc\ length = \frac{3}{4} \pi\ in$

Therefore the arc length of the sector is $\frac{3}{4} \pi\ in$