2024 IGCSE Additional Mathematics October/November 0606/23 Q4

2024 IGCSE Additional Mathematics October/November 0606/23 Q4

8 marks

The diagram shows a design for a logo. The logo is a sector of a circle, radius \(r\text{ cm}\), with angle \(\alpha\) radians.

The area of the logo is \(9\text{ cm}^2\).

  1. Show that the perimeter, \(P\text{ cm}\), of the logo is given by \(P=2r+\dfrac{18}r\).[3]
  2. Given that \(r\) can vary, find the stationary value of \(P\) and determine its nature.[5]

Solution:

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Answer:(a) \(P=2r+\dfrac{18}r\). (b) Minimum \(P=12\text{ cm}\), at \(r=3\text{ cm}\).

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