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If h, C, V are respectively the height, the curved surface and the volume of a cone, then 3πVh³ – C²h² + 9V² = ?
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- 0
- 3
- 1/2
- 11
- 0
Correct Option: A
Slant height = l units Radius = r units
| ∴ l = √r² + h² , V = | πr²h , C = πrl | |
| 3 |
∴ 3πVh³ - C²h² + 9V²
| = 3π × | πr²h × - (πrl)²h² + |  | πr²h |  | ||
| 3 | 3 |
= π²r²h4 - π²r²l²h² + π²r4h²
= π²r²h4 - π²r²h²(r² + h²) + π²r4h²
= π²r²h4 - π²r4h² - π²r4h²
= 0
