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    Question

    A regular tetrahedron has a lateral surface area of 108√3

    cm². Calculate its volume.
    A 250√2 cm³ Correct Answer Incorrect Answer
    B 144√2 cm³ Correct Answer Incorrect Answer
    C 200√2 cm³ Correct Answer Incorrect Answer
    D 350√2 cm³ Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the edge length of the tetrahedron be 's' cm

    Lateral surface area = 3 × (√3/4) × s²

    As given,

    108√3 = 3 × (√3/4) × s²

    ⇒ s² = 144

    ⇒ s = 12

    Volume = (√2/12) × s³

    = (√2/12) × 12 × 12 × 12

    = 144√2 cm³

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