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      Question

      A right circular cone has a height that is double its

      radius, and its volume is measured at 2,250π cm³. If the radius is reduced to one-third and the height to half of their original sizes, what would be the new volume of the cone? 
      A 225π cm³ Correct Answer Incorrect Answer
      B 375π cm³ Correct Answer Incorrect Answer
      C 125π cm³ Correct Answer Incorrect Answer
      D 250π cm³ Correct Answer Incorrect Answer

      Solution

      Let the radius of right circular cone be 'R' cm. So, height of cone = '2R' cm Volume of a right circular cone = (1/3) X π X (radius) 2 X height So, (1/3) X π X R2 X 2R = 2,250π Or, R3 = 3,375 Or, 'R' = 15 cm Height of cone = 2 X 15 = 30 cm New radius of cone = (15/3) = 5 cm New height of cone = (30/2) = 15 cm So, required volume = (1/3) X π X 52 X 15 = 125π cm3

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