Consider the cone x^2 + y^2 =z^2/4(z ≥ 0) as a wine glass full of wine. We put a (heavy) ball with radius 2 in
the glass such that it touches (is tangent to) the glass and has center located on the z-axis. Let sphere S be the
shell of the ball. Certainly, the radius of S is also 2.
(1). Find the equation of the sphere S.
(2). Find the volume of wine in the glass under the ball. Provide the entire answer in JSON format.
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