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Find the volume of a tetrahedron whose height is 6√3 cm?
1. 250 cm3
2. 225 cm3
3. 216 cm3
4. 243 cm3

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Correct Answer - Option 4 : 243 cm3

Given:

Height of tetrahedron = 6√3 cm

Formula used:

Height of tetrahedron = (√2/√3) × side

Volume of tetrahedron = (√2/12) × side3

Calculation:

∵ Height of tetrahedron = (√2/√3) × side

⇒ 6√3 = (√2/√3) × side

⇒ [(6√3) × √3]/√2 = side

⇒ Side = 18/√2 cm

∴ Volume of tetrahedron = (√2/12) × side3

= (√2/12) × (18/√2)3

= (√2 × 18 × 18 × 18)/(12 × √2 × √2 × √2)

= 243 cm3

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