A uniform solid cylinder has radius $0.7\text{ m}$ and height $h\text{ m}$. A uniform solid cone has base radius $0.7\text{ m}$ and height $2.4\text{ m}$. Both the cylinder and the cone are in equilibrium, with a circular face resting on a horizontal plane. The plane is then inclined from the horizontal, and the angle of inclination, $\theta^\circ$, is increased slowly until the cone is just on the point of toppling.
(i)[2]
Determine the value of $\theta$ when the cone is just about to topple.
(ii)[2]
The cylinder is known not to topple; determine the maximum possible value of $h$.
(iii)[5]
The plane is restored to a horizontal position, and the cone is attached to one end of the cylinder so that their faces coincide. The weight of the cylinder is three times the weight of the cone. The cone's curved surface is placed on the horizontal plane (see diagram). Since the solid topples immediately, determine the smallest possible value of $h$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $\tan \theta = \frac{0.7}{2.4/4}$” …