Question

Find the length of the darkened arc. Leave your answer in terms of pi.​

Answer 1

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.

Step-by-step 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 2

`(15 )/(4) \pi \:`

Step-by-step explanation:

Radius of circle (r) = 18/2 = 9 ft

Central angle = 180° - 30° = 150°

`length \: of \: arc \\ = (150 \degree)/(360 \degree) * 2\pi \: r \\ \\ = (150 \degree)/(360 \degree) * 2 * \pi \: * 9\\ \\ = (5 )/(12 ) * 18 * \pi \: \\ \\ = (5 )/(4) * 3* \pi \:\\ \\ = (15 )/(4) \pi \:`