Question

In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 2π/3 radians.



What is the length of the arc?

Answer 1

Answer:

length of the arc = 6.28 ft

Step-by-step explanation:

$r = 3 \: ft \\ central \: angle \: ( \theta) = \frac{2\pi^{c} }{3} = 120 \degree \\ \\ l = \frac{ \theta}{360 \degree} \times 2\pi \: r \\ \\ l = \frac{ 120 \degree}{360 \degree} \times 2 \times 3.14 \times 3\\ \\l = \frac{ 1}{3} \times 6.28 \times 3\\ \\ l = 6.28 \: ft$