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:

Arc length is $\dfrac{3\pi }{4}\ \text{inches}$

Step-by-step 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 :

$\dfrac{\text{arc length}}{\text{circumference}}=\dfrac{\theta}{360}$

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

$\theta=15^{\circ}$

$\dfrac{x}{18\pi }=\dfrac{15}{360}\\\\\dfrac{x}{18\pi }=\dfrac{1}{24}\\\\x=\dfrac{18\pi }{24}\\\\x=\dfrac{3\pi }{4}\ \text{inches}$

Hence, the correct option is (b).