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A uniform solid cone has vertical height 20 cm and base radius \(r \mathrm {~cm}\). It is placed with its axis vertical on a rough horizontal plane. The plane is slowly tilted until the cone topples when the angle of inclination is \(24 ^ { \circ }\) (see diagram).
- Find \(r\), correct to 1 decimal place.
A uniform solid cone of vertical height 20 cm and base radius 2.5 cm is placed on the plane which is inclined at an angle of \(24 ^ { \circ }\).
- State, with justification, whether this cone will topple.