Floating Cone without ice cream!

A right circular cone of semi-vertical angle α \alpha . can float vertex down in water with generator vertical and the base just clear of the water as shown in the figure.If the relative density of the material of the cone is given by c o s ( p / q ) ( l ( α cos^{(p/q)}(l(\alpha )). Find l+p+q.


The answer is 7.

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