# A Ball in a Cone? Is that something new?

Geometry Level pending

There's a ball in a cone. Let the radius of the ball is $$r$$ cm and the radius of cone is $$R$$ cm.

The height of the cone is $$h$$ cm and the lateral height (the length of a line segment from the apex of the cone along its side to its base) is $$l$$ cm.

If

$$R+h= 112$$

$$h+l= 144$$

$$l+R = 128$$

What is the ratio between the volume of ball and the volume of cone?

The answer is the form of $$x:y$$. Submit your answer as $$(x^2+3xy+y^2)(x^2+xy+y^2)$$.

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