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AP EAMCET20224 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

Options

  1. A2 : 1
  2. B1 : 2
  3. C2 : 3
  4. D3 : 2

Correct answer

A. 2 : 1

Step-by-step solution

For a closed cylinder let the height be h and base radius be r . Volume, V = π r 2 h i.e. h = V πr 2 Now, surface area, S = 2 πrh + 2 πr 2 = 2 πr V πr 2 + 2 πr 2 = 2 V r + 2 πr 2 For least surface area, d S d r = 0 ⇒ - 2 V r 2 + 4 πr = 0 ⇒ V = 2 πr 3 Hence, h = 2 r ⇒ h : r = 2 : 1

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