Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A uniform solid cone is $1.2\,\text{m}$ high and has a base radius of $0.5\,\text{m}$. A uniform object is formed by boring a cylindrical hole of radius $0.2\,\text{m}$ through the cone along its axis of symmetry (see diagram).
(i)[4]
Show that the height of the object is $0.72\,\text{m}$ and that the volume of the cone removed by the drilling is $0.0352\pi\,\text{m}^3$.
[The volume of a cone is $\frac{1}{3}\pi r^2 h$.]
(ii)[6]
Find the distance of the centre of mass of the object from its base.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies similar triangles to obtain the conical tip height $= 1.2\times\dfrac{0.2}{0.5} = 0.48$” …