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A volume is described as follows: 1. the base is the region bounded by x=−y2+8y+50x=-y2+8y+50 and...

A volume is described as follows:
1. the base is the region bounded by x=−y2+8y+50x=-y2+8y+50 and x=y2−24y+146x=y2-24y+146;
2. every cross section perpendicular to the y-axis is a semi-circle.

Find the volume of this object.

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