Calculate the volume swept out when the top half of the elliptical region bounded by...

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Problem

Work the problem by substituting a=4 and b=3, then solve usin direct integration.

Not sure where to get started here. Some guidance would be appreciated. Pretty sure this just requires creating the equation and just straight solving but I can't seem to figure it out.

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Hint: Use the distance from the x-axis of the ellipse as the radius of a circle.