Center of mass on the edge Consider the constant-density solid {(ρ, φ, θ): 0 < a ≤ ρ ≤ 1, 0 ≤ φ ≤ π/2, 0 ≤ θ ≤ 2 π} bounded by two hemispheres and the xy-plane.
a. Find and graph the z-coordinate of the center of mass of the plate as a function of a.
b. For what value of a is the center of mass on the edge of the solid?
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