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AP EAMCET202023 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

If the curved surface area of right circular cylinder inscribed in a sphere of radius 22 cm is maximum then height of the cylinder will be

Options

  1. A11 2   cm
  2. B11 2   cm
  3. C( 0 . 22 ) 2 m
  4. D( 0 . 11 ) 2 m

Correct answer

B. 11 2   cm

Step-by-step solution

Curved surface area = 2 πrh A = 2 πh ( 484 - h 2 ) r 2 + h 2 = ( 22 ) 2 ⇒ d A d h = 2 π 484 - h 2 + - 2 h 2 2 484 - h 2 = 0 ⇒ 484 - h 2 - h 2 = 0 ⇒ h 2 = 242 ⇒ h = 11 2   cm

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