The accompanying figure on the next page shows the solid that is bounded above by the surface
(a) By symmetry, the centroid of the solid lies on the z-axis. Make a conjecture about the behavior of the z-coordinate of the centroid as
(b) Find the z-coordinate of the centroid, and check your conjecture by calculating the appropriate limits.
(c) Use a graphing utility to plot the z-coordinate of the centroid versus a, and use the graph to estimate the value of a for which the centroid is
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