A cone of height 9cm has a volume of n cm³ and a curved surface area of n cm² find the vertical angle of a cone.

so, you have

1/3 πr^2 * 9 = πrs
Now, s^2 = r^2+9^2, so
3πr = π√(r^2+81)
9r^2 = r^2+81
8r^2 = 81
r = 9/√8
So the vertical angle θ is such that
tanθ = h/r = √8
θ = 72.55°