Correct Answer - Option 4 : 243 cm
3
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