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 ∛2 Correct Answer Incorrect Answer
    C 2√2 Correct Answer Incorrect Answer
    D √2/2 Correct Answer Incorrect Answer

    Solution

    According to the question, π(r + l)r = 4πr^2 ⇒ (r + l) = 4r ⇒ l = 3r l^2 = H^2 + r^2 ⇒ 9r^2 = H^2 + r^2 ⇒ 8r^2 = H^2 ⇒ H = 2√2r Now, Diameter = 2r So, Height is 2√2r/2r = √2 times ∴ Required answer is √2

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