Answer:
Formula for the Arc length is given by:
[tex]\text{Arc length} = 2 \pi r \cdot \frac{\theta}{360^{\circ}}[/tex]
As per the statement:
radius of circle(r) = 6 units
Angle ([tex]\theta[/tex]) = [tex]\frac{7 \pi}{8}[/tex] radian
Use conversion:
[tex]1 rad = \frac{180}{\pi}[/tex]
[tex]\frac{7 \pi}{8}[/tex] = [tex]\frac{180}{\pi} \cdot \frac{7 \pi}{8} = \frac{1260}{8} = 157.5^{\circ}[/tex]
then;
substitute these given values we have;
Use value of [tex]\pi = 3.14[/tex]
[tex]\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot \frac{157.5^{\circ}}{360^{\circ}}[/tex]
or
[tex]\text{Arc length} = 2\cdot 3.14 \cdot (6) \cdot 0.4375[/tex]
Simplify:
[tex]\text{Arc length}=16.485[/tex]
Therefore, the arc length of the arc substended in a circle with radius 6 units an angle of 7 pi/8 is 16.485 units
