Question
If the lateral surface area of a regular tetrahedron is 432√3 cm², then find its volume.
Solution
ATQ,
Let the side of the tetrahedron be 's' cm
Lateral surface area = 3 × (√3/4) × s²
ATQ;
432√3 = 3 × (√3/4) × s²
⇒ s² = 576
⇒ s = 24
Volume = (√2/12) × s³
= (√2/12) × 24 × 24 × 24
= 1152√2 cm³
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