A gold lamina in the shape of a bowl is denser at the bottom than top. It lies along the upper hemisphere x² +y² + z² = 1,z > 0. Calculate the mass of gold needed for the bowl as a surface given that the density at a point (x, y, z) on the surface of the hemisphere is 8(x,y,z) = (2 – z)K kg/mm³ for constant K. Calculate the average density of this gold lamina in the shape of a bowl.

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