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A closed cylindrical can has to be made with 100 m 2 of plastic. If its volume is maximum, then the ratio of its radius to the height is

Options

  1. A1 : 1
  2. B1 : 2
  3. C2 : 1
  4. D2 : 1

Correct answer

B. 1 : 2

Step-by-step solution

Let x be the radius and y be the height ∵ 2 π x 2 + x y = 100 ⇒ 50 π x - x = y Volume, V = π x 2 y = π 50 x π - x 3 d V d x = 0 ⇒ x = 5 2 3 π and y = 10 2 3 π ∴ x y = 1 2

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