Question

A sector has a radius of 15 centimeters and an angle of 48°. Find its arc length.A. 6.5 cmB. 12.6 cmC. 16.1 cmD. 13.6 cm

Answer 1

The formula for the length of an arc of a sector is :

`L=(\theta)/(360)*2\pi r`

where:

`\begin{gathered} \theta=\sec tor\text{ angle} \\ r=\text{radius of the circle} \end{gathered}`

Since we are given:

we have that:

`\begin{gathered} L=(\theta)/(360)*2\pi r \\ \Rightarrow L=(48)/(360)*2\pi(15) \end{gathered}`
`L=(2)/(15)*30\pi`
`\Rightarrow L=(60\pi)/(15)`
`\Rightarrow L=4\pi`
`\begin{gathered} \Rightarrow L=4*3.14=12.56 \\ \Rightarrow L=12.6\text{ cm} \end{gathered}`

Thus, correct answer: Option B