When is the bottom of a Pint Glass exposed?

Geometry Level 5

A pint glass constitutes the top portion of an inverted cone, and the ratio of the heights of glass to cone is \( q \). When the height of the beer is \(\dfrac7{16} \) of the height of the glass when it's upright, the bottom of the glass is only just completely covered by beer when it's tipped to the rim.

If \(q\) can be expressed in the form \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\). If it cannot, yes it can.

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