2025 CGSS PRELIMS P1 Q10

2025 CGSS PRELIMS P1 Q10

Secondary 4
4 marks

A pet dish bowl is in the shape of a frustum, as shown in the diagram. It is formed by removing a smaller cone from the top of a larger cone. The smaller cone is similar to the original cone, and its volume is \(\dfrac38\) of the volume of the original cone. The original cone has a height of \(40\text{ cm}\).

  1. Find \(h\), the height of the frustum.[2]
  2. Given that the curved surface area of the frustum is \(966\text{ cm}^2\), find the curved surface area of the smaller cone.[2]

Solution:

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Answer:(a) \(h=40[1-(3/8)^{1/3}]\approx11.2\text{ cm}\). (b) \(S\approx1.05\times10^3\text{ cm}^2\) (3 s.f.).

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