A tilted cup of water - part 2
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 ?