Geometric Similarity: Length, Area, and Volume Ratios

The diagram shows a solid cone that is cut into two sections, \(P\) and \(Q\), such that section \(P\) is a cone similar to the original cone.
The curved surface area of cone \(P\) is \(90\) cm\({}^2\), and the curved surface area of the original cone is \(160\) cm\({}^2\).

1. If the height of cone \(P\) is \(15\) cm, calculate the height, \(x\) cm, of the original cone.
2. Find the ratio of the volume of the original cone to the volume of cone \(P\).
3. Given that the mass of cone \(P\) is \(500\) g, find the mass of section \(Q\), correcting your answer to \(3\) significant figures.