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      Question

      The total surface area of a solid right circular cone is

      equal to that of a sphere of the same radius. The height of the cone is how many times the diameter of the sphere?
      A √2 Correct Answer Incorrect Answer
      B βˆ›2 Correct Answer Incorrect Answer
      C 2√2 Correct Answer Incorrect Answer
      D √2/2 Correct Answer Incorrect Answer

      Solution

      According to the question, Ο€(r + l)r = 4Ο€r^2 β‡’ (r + l) = 4r β‡’ l = 3r l^2 = H^2 + r^2 β‡’ 9r^2 = H^2 + r^2 β‡’ 8r^2 = H^2 β‡’ H = 2√2r Now, Diameter = 2r So, Height is 2√2r/2r = √2 times ∴ Required answer is √2

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