step 1
Find out the circumference of the circle
[tex]C=Pi*D[/tex]
where
D=2(4)=8 km ----> the diameter is two times the radius
substitute
[tex]\begin{gathered} C=pi*8 \\ C=8pi\text{ km} \end{gathered}[/tex]
Remember that the circumference subtends a central angle of 360 degrees
so
Applying proportion
Find out the arc length by a central angle of 135 degrees
[tex]\begin{gathered} \frac{8pi}{360^o}=\frac{x}{135^o} \\ \\ x=\frac{8p\imaginaryI}{360^{o}}*135^o \end{gathered}[/tex]
x=3pi km
therefore
The answer is 3pi km
