Answer:
37.89 cm
Step-by-step explanation:
The length of an arc can be calculated using the formula;
[tex]l = \frac{ \theta}{360 \degree} \times 2 \pi \: r[/tex]
The central angle of the sector is given as
[tex] \theta = 190 \degree[/tex]
The arc length is given as l=40π
We want to find the radius of the circle.
We substitute and solve for r.
[tex]40\pi= \frac{190 \degree}{360 \degree} \times 2 \pi \: r[/tex]
Simplify:
[tex]40= \frac{19}{18} \times\: r[/tex]
[tex]r = \frac{18 \times 40}{19} [/tex]
[tex]r = 37.89[/tex]
