Finding Volumes of Solids
Find the volumes of the solids (see figures) generated if the upper half of the ellipse is revolved about (a) the x-axis to form a prolate spheroid (shaped like a football) and (b) the y-axis to form an oblate spheroid (shaped like half of a candy).
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Consider the graph of , as shown in the figure. Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line .
Comparing Volumes
The region in the figure is revolved about the indicated axes and line. Order the volumes of the resulting solids from least to greatest. Explain your reasoning.
(a) x-axis (b) y-axis (c)
Equal Volumes
Let and be the volumes of the solids that result when the plane region bounded by is revolved about the x-axis and the y-axis respectively. Find the value of c for which .
