Don't Spill it!

Geometry Level 4

A cylindrical glass of radius 3 is filled with water until its height reaches 11, as shown above left.

Now, if the cylinder is tilted such that it forms an angle of \(\theta\) with the ground with \(\cos \theta = \frac{4}{5}\), what is the new height \(h\)?

\(\)
Clarification: The cylinder is so long that no water spills over.

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