A homogeneous cone of height h = 12 in. and with a base diameter d = 6

Question:

A homogeneous cone of height h = 12 in. and with a base diameter d = 6 in. is attached as shown to a cord AB. Knowing that the angles that cord AB and the axis BC of the cone form with the vertical are, respectively, β = 45? and θ = 30?, and that the cone processes at the constant rate φ = 8 rad/s in the sense indicated, determine

(a) The rate of spin ψ of the cone about its axis BC,

(b) The length of cord AB.