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      Question

      A pyramid has a square base with a height of 12 cm. Each

      of the pyramid's faces is an equilateral triangle, and the area of each face is 64√3 cm². Find the volume of the pyramid.
      A 3072 cubic m Correct Answer Incorrect Answer
      B 512 cubic m Correct Answer Incorrect Answer
      C 2048 cubic m Correct Answer Incorrect Answer
      D 1024 cubic m Correct Answer Incorrect Answer

      Solution

      Length of each side of the base of the pyramid = Length of base of each triangular face Let the length of base of each triangular face be 'a' cm. So, 64√3 = (√3/4) X a2 Or, a2 = 256 So, a = 16 {Since, length of side cannot be negative} So, area of base of the pyramid = 16 X 16 = 256 cm2 So, volume of pyramid = 256 X 12 X (1/3) = 1024 cm3

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