Question: (a) (5 points) A solid sphere \(S\) of radius \(a\) is placed above the xy-plane so it is tangent at the origin and its diameter lies along the \(z\) -axis. Give its equation in spherical coordinates.

(b) (5 points) Give the equation of the horizontal plane \(z=a\) in spherical coordinates.

(c) (5 points) Set up a triple integral in spherical coordinates which gives the volume of the portion of the sphere \(S\) lying above the plane \(z=a\). Give the integrand and limits of integration, but do not evaluate.

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