[You may assume that the volume of a cone of height $$\(h\)$$ and base radius $$\(r\)$$ is $$\(\frac{1}{3} \pi r^{2} h\)$$.] A uniform solid right circular cone $$\(C\)$$, with vertex $$\(V\)$$, has base radius $$\(r\)$$ and height $$\(h\)$$. (a) Show that the centre of mass of $$\(C\)$$ is $$\(\frac{3}{4} h\)$$ from $$\(V\)$$ (4) A solid $$\(F\)$$, shown below in Figure 4, is formed by removing the solid right circular cone $$\(C^{\prime}\)$$ from $$\(C\)$$, where cone $$\(C^{\prime}\)$$ has height $$\(\frac{1}{3} h\)$$ and vertex $$\(V\)$$ (b) Show that the distance of the centre of mass of $$\(F\)$$ from its larger plane face is $$\(\frac{3}{13} h\)$$ (5) The solid $$\(F\)$$ rests in equilibrium with its curved surface in contact with a horizontal plane. (c) Show that $$\(13 r^{2} \leqslant 17 h^{2}\)$$ (5)

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