Let H be the hemispherical shell x2 + y2 + (z - 1)2 = 1, 0 ( z (a) ((x, y, z) is the time required for a particle dropped from (x, y, z) to reach the level z = 0.
(b) ((x, y, z) is the area of the inside of H (assumed opaque) that can be seen from (x, y, z).
(c) ((x, y, z) is the area of the shadow of Hon the xy-plane due to a point light source at (x, y, z).
(d) ((x, y, z) is the distance along the shortest path from (x, y, z) to (0,0,0) that does not penetrate H.

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