Question:
In a circle with a radius of 12.6 ft, an arc is intercepted by a central angle of 2π/7 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
Answer:
Arc length is 11.30 feet
Solution:
Given that,
Radius of circle = 12.6 feet
Central angle = [tex]\frac{2 \pi }{7}[/tex] radians
To find: Arc length
The arc length of a circle of radius "r" when central angle given in radians is:
[tex]s = r \times \theta[/tex]
Where,
s is the arc length
r is the radius
[tex]\theta[/tex] is the central angle in radians
Substituting the values we get,
[tex]s = 12.6 \times \frac{2 \times \pi }{7}\\\\s = 12.6 \times \frac{2 \times 3.14 }{7}\\\\x = 11.304 \approx 11.30[/tex]
Thus, arc length is 11.30 feet
