Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A solid cone of uniform density has height $1.2\,\text{m}$ and base radius $0.5\,\text{m}$. 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]
Demonstrate that the height of the object is $0.72\,\text{m}$ and that the volume of the cone removed by the drilling is $0.0352\pi\,\text{m}^3$.
[Use the cone-volume formula $\tfrac{1}{3}\pi r^2 h$].
(ii)[6]
Determine the distance from the base to the centre of mass of the object.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The height of the conical tip is $1.2 \times \dfrac{0.2}{0.5} = 0.48$” …