Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A single uniform body is formed by joining the flat base of a solid hemisphere to the flat base of a solid cone, so that the body has an axis of symmetry. The cone has base radius $0.3\,\text{m}$, and the hemisphere has radius $0.2\,\text{m}$. The body is resting on a horizontal plane, with point $A$ on the curved surface of the hemisphere and point $B$ on the rim of the cone in contact with the plane (see diagram).
(i)[3]
Assuming that the object is just about to topple about $B$, find how far the centre of mass of the object is from the base of the cone.
(ii)[3]
If, instead, the object is just on the point of toppling about $A$, calculate the height of the cone.
[A cone has volume $\frac{1}{3}\pi r^2 h$. A hemisphere has volume $\frac{2}{3}\pi r^3$.]
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\cos\theta = \dfrac{0.2}{0.3}$” …