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      Question

      A cone and a hemisphere have the same base radius and

      the same height. If the total volume of both is 2,160 cm┬│, find the radius.
      A 8.8 cm Correct Answer Incorrect Answer
      B 10.4 cm Correct Answer Incorrect Answer
      C 12.6 cm Correct Answer Incorrect Answer
      D 14.8 cm Correct Answer Incorrect Answer
      E 20 cm Correct Answer Incorrect Answer

      Solution

      Volume of cone = (1/3)╧Аr┬▓h Volume of hemisphere = (2/3)╧Аr┬│ Total volume = (1/3)╧Аr┬▓h + (2/3)╧Аr┬│ = 2160 Since base radius and height are the same, let h = r. (1/3)╧Аr┬│ + (2/3)╧Аr┬│ = 2160 (1/3 + 2/3)╧Аr┬│ = 2160 ╧Аr┬│ = 2160 r┬│ = 2160 / ╧А = 2160 / 3.14 тЙИ 687.58 r тЙИ 8.8 cm Correct Option: a) 8.8 cm

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