2
\includegraphics[max width=\textwidth, alt={}, center]{d3609757-50ae-4c68-8992-4304867a2d84-2_551_519_1231_813} A uniform solid cone has height 30 cm and base radius \(r \mathrm {~cm}\). The cone is placed with its axis vertical on a rough horizontal plane. The plane is slowly tilted and the cone remains in equilibrium until the angle of inclination of the plane reaches \(35 ^ { \circ }\), when the cone topples. The diagram shows a cross-section of the cone.

1. Find the value of \(r\).
2. Show that the coefficient of friction between the cone and the plane is greater than 0.7 .