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    Question

    If the lateral surface area (3

    faces) of a regular tetrahedron is 75√3 cm2, find its volume.
    A (120√2)/5 cm³ Correct Answer Incorrect Answer
    B (150√2)/3 cm³ Correct Answer Incorrect Answer
    C (250√2)/3 cm³ Correct Answer Incorrect Answer
    D (100√2)/3 cm³ Correct Answer Incorrect Answer

    Solution

    ATQ, LSA = 3*(√3/4)*a2 = (3√3/4)*a2 (3√3/4)*a2 = 75√3 (3/4)*a2 = 75 a2 = 100 a = 10 cm Volume: V = a3/(6√2) V = 103/(6√2) = 1000/(6√2) = 500/(3√2) = (250√2)/3 cm3 FINAL ANSWER: (250√2)/3 cm3

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