Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A single uniform body is formed by fixing the flat base of a solid hemisphere to the flat base of a solid cone, with the result that the shape has an axis of symmetry. The cone has base radius $0.3\ \text{m}$, while the hemisphere has radius $0.2\ \text{m}$. The body is rested on a horizontal plane so that a point $A$ on the curved surface of the hemisphere and a point $B$ on the rim of the cone are in contact with the plane (see diagram).
(i)[3]
If the object is just about to topple about $B$, determine the distance of the object’s centre of mass from the base of the cone.
(ii)[3]
If instead the object is just about to topple about $A$, calculate the cone’s height. [The volume of a cone is $\tfrac{1}{3}\pi r^2 h$. The volume of a hemisphere is $\tfrac{2}{3}\pi r^3$.]
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme.