A cone with hemispherical and conical removals
A cone with hemispherical and conical removals
Secondary 2
8 marks
TGM Original Questions
Optional extension
A cone has base radius 9 cm and height 12 cm. A hemispherical cavity of radius 3 cm is removed from its base. Use \(\pi=3.142\).
- Find the cone slant height.[2]
- Find remaining volume.[2]
- Find total exposed surface area.[2]
- A smaller similar cone of height 4 cm is then removed from the vertex; find its volume.[2]
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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