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Each edge of a regular tetrahedron is 3 cm, then its volume is
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9√2 c.c. 4 - 27√3 c.c.
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4√2 c.c. 9
- 9√3 c.c.
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Correct Option: A
| Area of the tetrahedron = | area of base × height | |
| 3 |
| Area of the base = | × (side)² | |
| 4 |
| = | × 3 × 3 = | cm² | ||
| 4 | 4 |
Now, length of the perpendicular in the equilateral triangle
| = √3² - |  |  | ² | |
| 2 |
| = √9 - | = | cm | ||
| 4 | 2 |
| ∴ Height = √ | | | ² | - | | | ² | ||
| 2 | 2 |
| = √ | - | = √6 cm. | ||
| 4 | 4 |
| ∴ Required area = | × | × √6 = | cu.cm. | |||
| 3 | 4 | 4 |
