In Euclidean space, take the point N(0, 0, 1) on the sphere S with radius 1 centered in the origin. For moving points P, Q on S such that NP \equal{} NQ and \angle{PNQ} \equal{} \theta \left(0 < \theta < \frac {\pi}{2}\right), consider the solid figure T in which the line segment PQ can be passed.
(1) Show that z coordinates of P, Q are equal.
(2) When P is on the palne z \equal{} h, express the length of PQ in terms of θ and h.
(3) Draw the outline of the cross section by cutting T by the plane z \equal{} h, then express the area in terms of θ and h.
(4) Pay attention to the range for which h can be valued, express the volume V of T in terms of θ, then find the maximum V when let θ vary. calculusintegrationgeometry3D geometrysphereanalytic geometrycalculus computations