Let the radii of the circular ends be r1 cm and r2 cm.
Given:
Curved surface area of the frustum of the cone = 180 cm2
Also,
Circumference of the small end (C1) = 6 cm
2 r1 = 6
r1=
And,
Circumference of the large end (C2) = 18 cm
2 r2 = 18
r2=
Now,
Curved surface area of the frustum of the cone = (r1 + r2)l
180 =
180 = 12l
l = 15 cm
Thus, the slant height of the frustum of the cone is 15 cm.