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    Question

    The lateral surface area of a regular tetrahedron is 75√3

    cm². Determine the volume of the tetrahedron.
    A 250√2 cm³ Correct Answer Incorrect Answer
    B 175√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

    ATQ;

    75√3 = 3 × (√3/4) × s²

    Or, s² = 100

    So, s = 10

    Volume = (√2/12) × s³

    = (√2/12) × 10 × 10 × 10

    = 250√2 cm³

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