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There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of this pyramid is of length 5a/2 cm, then the volume of this pyramid is
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- 3a³ cm³
- 3√2a³ cm³
- 3√3a³ cm³
- 6a³ cm³
- 3a³ cm³
Correct Option: C
| Area of the base = 6 × | × (2a)² | |
| 4 |
| = 6 × | × 4² = 6√3² sq.cm. | |
| 4 |
| Height = √ |  |  | ² | - (2a)² | |
| 2 |
| = √ | a² - 4a² | |
| 4 |
| = √ | ||
| 4 |
| = | a cm. | |
| 2 |
| ∴ Volume of pyramid = | × area of base × height | |
| 3 |
| ∴ Volume of pyramid = | × 6√3a² × | a | ||
| 3 | 2 |
= 3√3a³cm³
