(i)[3]
Find $r$.
(ii)[2]
Show that the coefficient of friction between the cone and the plane exceeds $0.7$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A uniform solid cone of height $30\text{ cm}$ and base radius $r\text{ cm}$ stands with its axis vertical on a rough horizontal plane. The plane is then gradually tilted, and the cone stays in equilibrium until the plane’s angle of inclination reaches $35^\circ$, at which point the cone topples. The diagram shows a cross-section through the cone.