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2021 Geo Div 2 P4

Source:

March 2, 2021
geometry

Problem Statement

A 252\sqrt5 by 454\sqrt5 rectangle is rotated by an angle θ\theta about one of its diagonals. If the total volume swept out by the rotating rectangle is 62π62\pi, find the measure of θ\theta in degrees.
Proposed by Connor Gordon
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