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JEE Main2012MathematicsApplication of DerivativesActual

If a metallic circular plate of radius 50 ~cm is heated so that its radius increases at the rate of 1 ~mm per hour, then the rate at which, the area of the plate increases (in cm ^2 / hour) is

Options

  1. A5
  2. B10
  3. C100
  4. D50

Correct answer

B. 10

Step-by-step solution

Let A= r ^2 be area of metalic circular plate of r=50 ~cm . Also, given d r d t =1 ~mm = 1 10 ~cm aligned & A= r^2 & d A d t =2 r d r d t =2 50 1 10 =10 aligned Hence, area of plate increases in 10 cm ^2 / hour.

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