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    Question

    If the lateral surface area of a regular tetrahedron is

    108√3 cm², what is its volume?
    A 150√2 cm³ Correct Answer Incorrect Answer
    B 144√2 cm³ Correct Answer Incorrect Answer
    C 252√2 cm³ Correct Answer Incorrect Answer
    D 250√2 cm³ Correct Answer Incorrect Answer

    Solution

    ATQ,

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

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

    ATQ;

    108√3 = 3 × (√3/4) × s²

    Or, s² = 144

    So, s = 12 (Since, length cannot be negative therefore we will take the positive root only)

    Volume of tetrahedron = (√2/12) × s³

    = (√2/12) × 12 × 12 × 12

    = 144√2 cm³

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