A cone with hemispherical and conical removals

A cone with hemispherical and conical removals

Secondary 2
TGM Original Questions

A cone has base radius 9 cm and height 12 cm. A hemispherical cavity of radius 3 cm is removed from its base. Use \(\pi=3.142\).

  1. Find the cone slant height.
  2. Find remaining volume.
  3. Find total exposed surface area.
  4. A smaller similar cone of height 4 cm is then removed from the vertex; find its volume.

Solution:

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Answer:(a) \(15\) cm; (b) \(961.45\text{ cm}^3\); (c) \(706.95\text{ cm}^2\); (d) \(37.70\text{ cm}^3\).

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