1st arc: 15π cm (18cm radius, 150° angle). 2nd arc: 14π/3 m (20m radius, 210° angle). Both lengths proportional to their central angles.
The lengths of the arcs can be found using the formula:
`s = r * θ`
where:
* `s` is the arc length
* `r` is the radius of the circle
* `θ` is the central angle of the arc, in radians
In the first arc, the central angle is 150 degrees. Converting this to radians, we get:
`θ = 150° * π/180° = 5π/6`
Substituting the values of `r` (18 cm) and `θ` into the formula, we get the length of the first arc:
`s₁ = 18 cm * 5π/6 = 15π cm`
In the second arc, the central angle is 210 degrees. Converting this to radians, we get:
`θ = 210° * π/180° = 7π/6`
Substituting the values of `r` (20 m) and `θ` into the formula, we get the length of the second arc:
`s₂ = 20 m * 7π/6 = 14π/3 m`
Therefore, the lengths of the arcs are:
* First arc: 15π cm
* Second arc: 14π/3 m