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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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