9 0 90^{\circ} Tilt of a cup

Geometry Level 4

A cup in the shape of a conical frustum with bottom radius 2 2 and top radius 4 4 and a slant height of 10 10 , is filled to half its height with a liquid. Next, it is sealed at the top, and then given a 9 0 90^{\circ} tilt so that the cup axis becomes horizontal. This is shown in the figure below. Find the distance between the axis of cup and the plane of the liquid surface after tilting. The required distance is indicated in the diagram as well.

The answer is 0.7952.

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