Question

Please help! :)

A sector of a circle has a central angle measuring 15 degrees and the radius of the circle measures 9 inches. What is the arc length of the sector? Express the answer in terms of Pi.

Answer 1

the answer is b/ the second option

Explanation:

Answer 2

Second option is correct

`Arc\ length = (3)/(4) \pi\ in`

Explanation:

Given:

Central angle = 15°

Radius of the circle = 9 in

Arc length = ?

Given formula is

`(Arc\ length)/(Circumfrance) = (n)/(360)`

Where n is the central angle of the sector.

Write the given formula for Arc length of the sector.

`Arc\ length = Circumfrance* (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* (n)/(360)`

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

`Arc\ length = 2\pi 9* (15)/(360)`

`Arc\ length = 18* \pi (15)/(360)`

`Arc\ length = (18* 15)/(360) \pi` ----------(
`(18)/(360)=(1)/(20)`)

`Arc\ length = (15)/(20) \pi`

Divide the numerator and denominator by 5.

`Arc\ length = (3)/(4) \pi\ in`

Therefore the arc length of the sector is
`(3)/(4) \pi\ in`