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.


\(R+h= 112\)

\(h+l= 144\)

\(l+R = 128\)

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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