Question

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.

Recall that StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction.
StartFraction 3 over 8 EndFraction pi inches
Three-fourths pi inches
1 and StartFraction 3 over 8 EndFraction pi inches
1 and one-half pi inches

Answer 1

Answer: B

Explanation:

Answer 2

Arc length is
`(3\pi )/(4)\ \text{inches}`

Explanation:

We have,

Central angle is 15 degrees and the radius of the circle measures 9 inches.

It is required to find the arc length of the sector.

The relation between arc length and the central angle is given by :

`\frac{\text{arc length}}{\text{circumference}}=(\theta)/(360)`

Circumference,
`C=2\pi r=18\pi`

`\theta=15^(\circ)`

`(x)/(18\pi )=(15)/(360)\\\\(x)/(18\pi )=(1)/(24)\\\\x=(18\pi )/(24)\\\\x=(3\pi )/(4)\ \text{inches}`

Hence, the correct option is (b).