A tilted cup of water - part 2

Geometry Level pending

A cup of water in the shape of a conical frustrum is tilted as shown. The base diameter is 5 cm, and the top diameter is 9 cm. The slant height is 12 cm. The cup contains one quarter of its volume in water. If the water level touches the edge of the base, find the angle $$\theta$$ (in degrees) that the cup has been turned from its upright position ?

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