Question

Hello, how are you? I would like you to help me solve this exercise, please!

Answer 1

Given

Formula for the length of an arc

`\begin{gathered} Measureof\text{Arc of a circle=}(\theta)/(360)*2\pi r \\ \\ \end{gathered}`

Parameters;

`\begin{gathered} \theta=?\text{ , r=1m} \\ \text{measure of arc =}(\pi)/(9) \end{gathered}`

We can substitute into the formula

`\begin{gathered} (\pi)/(9)=(\theta)/(360)*2*\pi*1 \\ \\ (\pi)/(9)=(2\theta\pi)/(360) \\ \text{cross multiply} \\ 18\theta\pi=360\pi \\ divide\text{ both sides by 18}\pi \\ (18\theta\pi)/(18\pi)=(360\pi)/(18\pi) \\ \theta=20^0 \end{gathered}`

Now, change to radian

`(\pi)/(180)*20^0=(20^0\pi)/(180^0)=(\pi)/(9)`

The final answer

`(\pi)/(9)`