Answer :
Final answer:
The length of the darkened arc can be found using the formula s = Δθr, where s is the length of the arc, Δθ is the angle of rotation, and r is the radius of curvature.
Explanation:
The length of the darkened arc can be found by using the formula for arc length: s = Δθr, where s is the length of the arc, Δθ is the angle of rotation, and r is the radius of curvature. In this case, the angle of rotation is 2π radians (since it is a complete revolution) and the radius is given. So, substituting these values into the formula, we have s = 2πr.
Answer:
[tex] \frac{15 }{4} \pi \:[/tex]
Step-by-step explanation:
Radius of circle (r) = 18/2 = 9 ft
Central angle = 180° - 30° = 150°
[tex]length \: of \: arc \\ = \frac{150 \degree}{360 \degree} \times 2\pi \: r \\ \\ = \frac{150 \degree}{360 \degree} \times 2 \times \pi \: \times 9\\ \\ = \frac{5 }{12 } \times 18 \times \pi \: \\ \\ = \frac{5 }{4} \times 3\times \pi \:\\ \\ = \frac{15 }{4} \pi \:[/tex]
