15 A segment of the line \(y = k x\) is rotated about the \(x\)-axis to generate a cone with vertex \(O\).
The distance of \(O\) from the centre of the base of the cone is \(h\).
The radius of the base of the cone is \(r\).
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15
- Find \(k\) in terms of \(r\) and \(h\).
15 - Use calculus to prove that the volume of the cone is
$$\frac { 1 } { 3 } \pi r ^ { 2 } h$$
\(16 \quad \mathbf { A }\) and \(\mathbf { B }\) are non-singular square matrices.