# 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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