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A plane divides a right circular cone into two parts of equal volume. If the plane is parallel to the base, then the ratio, in which the height of the cone is divided, is
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- 1 : ³√2
- 1 : 2
- 1 : ³√2 + 1
- 1 : ³√2 – 1
- 1 : ³√2
Correct Option: D
OA' = h units
AA' = H units
AB = R units
A'B' = r units.
A'B'|| AB
∠OA'B' = ∠OAB
∠OB'A' = ∠OBA
∴ ∆OAB ~ ∆OA;B;
| ∴ | = | |||
| OA | AB |
| ⇒ | = | |||
| H + h | R |
According to the question,
| πr²h = | πR²(H + h) - | πr²h | ||||
| 3 | 3 | 3 |
| ⇒ | πr²h = | πR²(H + h) | ||
| 3 | 3 |
| ⇒ 2 = | = | ||
| R² | h |
| ⇒ | = 2 | |
| h³ |
| ⇒ | = ³√2 | |
| h |
| ⇒ | + 1 = ³√2 | |
| h |
| ⇒ | = | ||
| h | 1 |
| ⇒ | = 1 : ³√2 - 1 | |
| H |
