2026 HGV P2 Q8

2026 HGV P2 Q8

Secondary 4
8 marks

The radius, \(r\) cm, and the height, \(h\) cm, of a solid circular cylinder vary in such a way that the volume of the cylinder is always \(1024\pi\) cm³.

  1. Express \(h\) in terms of \(r\).[2]
  2. Show that the total surface area, \(A\) cm², of the cylinder is given by \(A=2\pi r^2+\dfrac{2048\pi}{r}\).[2]
  3. Hence find the value of \(r\) for which the surface area of the cylinder is a minimum.[4]

Solution:

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Answer:(a) \(h=\dfrac{1024}{r^2}\). (b) \(A=2\pi r^2+\dfrac{2048\pi}{r}\) (shown). (c) \(r=8\text{ cm}\).

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