Question

Find the length of an arc of a circle whose central angle is 2.5 radians and its radius is 10inches.

Answer 1

The length of an arc of a circle is given by the formula:

`\begin{gathered} L\text{ = }(\theta)/(360)*2\pi r \\ \theta\text{ = 2. 5 radians} \\ r\text{ = 10 inches} \end{gathered}`

We need to convert 2. 5 radians to degrees

`\begin{gathered} 1\text{ radian =}(180)/(\pi) \\ 2.5\text{ radians =}(180)/(\pi)*2.5=(450)/(\pi) \end{gathered}`
`\begin{gathered} \text{ Therefore, L =}(450)/(360\pi)*2\pi*10 \\ L=25\text{inches} \end{gathered}`

Therefore, the length of the arc is 25inches.