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    Question

    If the lateral surface area of a regular tetrahedron is

    432√3 cm², then find its volume.
    A 1250√2 cm³ Correct Answer Incorrect Answer
    B 1152√2 cm³ Correct Answer Incorrect Answer
    C 2252√2 cm³ Correct Answer Incorrect Answer
    D 2350√2 cm³ Correct Answer Incorrect Answer

    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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