A sector with an area of 27 is cut out of a circle with a radius of 9. Find the arc length of the sector.

To solve this problem, remember that the length of the arc of the sector is proportional to its radius and the value of the central angle and is found by the formula p = π * r * n / 180, r is the radius of the arc, n is the central angle of the arc in degrees. We can calculate the central angle of the arc from the formula for the area of the sector. The area of the sector of a circle with an arc n is equal to the product of the area of a circle with a radius r by the ratio of the angle of the sector n to the angle of the full circle, 360 °.
S sector = π * r ^ 2 * n / 360.
27 = π * 9 * 9 * n / 360;
81π * n = 27 * 360 = 9720;
π * n = 9720/81;
π * n = 120.
Let’s calculate the length of the arc.
p = 120 * 9/180 = 1080/180 = 6 cm.
Answer: 6 cm.