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A cone is cut at mid point of its height by a frustum parallel to its base. The ratio between the two parts of cone would be
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- 1 : 1
- 1 : 8
- 1 : 4
- 1 : 7
- 1 : 1
Correct Option: D
∆ADE ~ ∆ABC
| ∴ | = | = | |||
| AB | BC | 2 |
| AD = AB ; DE = | BC | |
| 2 |
| Required ratio = | π(DE)² × AD | |||
| 3 | ||||
| π BC² × AB - | π (DE)² × AD | |||
| 3 | 3 | |||
| = | ||
| BC² × AB - DE² × AD |
| = | BC² × | AB | ||
| 4 | 2 | |||
| BC² × AB - | BC² × | |||
| 4 | 2 | |||
| = | = 1 : 7 | ||
| 8 | |||
| 1 - | |||
| 8 | |||
