A sector of radius 15 cm with a central angle of 216° is rolled up into a cone. Find the vertical height of the cone in cm.

Arc length = (216/360) × 2π × 15 = 18π cm, so the base radius $r$ satisfies 2π$r=18$π, giving $r=9$ cm. The sector's radius becomes the slant height, $l=15$ cm. Height = √$(15^2-9^2)=$ √144 = 12 cm.