Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
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, each resting with one circular face on a horizontal plane. The plane is then tilted, and its angle of inclination to the horizontal, $\theta^{\circ}$, is increased little by little 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]
Assuming the cylinder remains stable and does not 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 the plane faces line up. It is given that the weight of the cylinder is three times the weight of the cone. The curved surface of the cone is then placed on the horizontal plane (see diagram). Since the solid topples immediately, determine the least 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: “Apply $\tan \theta = \frac{0.7}{2.4/4}$” …