2026 IGCSE 0580 February/March P22 Q18

2026 IGCSE 0580 February/March P22 Q18

7 marks

The diagram shows a cone and a hemisphere.

The cone has radius \(r\text{ cm}\) and sloping edge \(12\text{ cm}\).

The hemisphere has radius \(4\text{ cm}\).

The total surface area of the cone is equal to the total surface area of the hemisphere.

  1. Show that \(r^2+12r-48=0\).[3]
  2. Find the exact value of the radius of the cone.
    Give your answer as a surd in its simplest form.[4]

Solution:

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Answer:(a) \(r^2+12r-48=0\). (b) \((2\sqrt{21}-6)\text{ cm}\).

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