Recasting a metal cone

Recasting a metal cone

IP 2
3 marks
TGM Original Questions

A solid metal cone of radius \(6\) cm and perpendicular height \(8\) cm is melted and recast into identical spheres of radius \(2\) cm, without loss of metal. Use \(V_{\mathrm{cone}}=\frac13\pi r^2h\) and \(V_{\mathrm{sphere}}=\frac43\pi r^3\).

  1. Find the volume of the cone in terms of \(\pi\).[1]
  2. Find the volume of one sphere in terms of \(\pi\).[1]
  3. Find the number of spheres formed.[1]

Solution:

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Answer:(a) \(96\pi\text{ cm}^3\) (b) \(\dfrac{32\pi}{3}\text{ cm}^3\) (c) \(9\)

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