Answer :
The formula to obtain the length of an arc(l) is,
[tex]l=\frac{\theta}{360^0}\times2\pi r[/tex]Given that
[tex]\begin{gathered} \theta=135^0 \\ \text{diameter}=10m,\text{ radius=}\frac{\text{diameter}}{2}=\frac{10}{2}=5 \\ \pi=\frac{22}{7} \end{gathered}[/tex]Therefore,
[tex]l=\frac{135}{360}\times2\times\frac{22}{7}\times5=\frac{29700}{2520}=11.7857m[/tex]