(i)[3]
Find the exact value of $r$.
(ii)[2]
Show that the coefficient of friction between the cone and the plane exceeds $0.7$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A solid cone of uniform density has height $30\,\text{cm}$ and base radius $r\,\text{cm}$. It is positioned with its axis vertical on a rough horizontal plane. The plane is then slowly tilted, and the cone remains in equilibrium until the angle of inclination reaches $35^\circ$, when it topples. The diagram shows a cross-section of the cone.