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AP EAMCET2012MathematicsApplication of Derivatives

If the volume of a sphere increases at the rate of 2 cm ^3 / s , then the rate of increase of its radius (in cm / s ), when the volume is 288 cm ^3 , is

Options

  1. A1 36
  2. B1 72
  3. C1 18
  4. D1 9

Correct answer

B. 1 72

Step-by-step solution

Given d V d t =2 cm ^3 / s Volume of sphere, V= 4 3 r^3 On differentiating w.r.t. t , we get aligned & d V d t = 4 3 3 r^2 d r d t & 2 =4 r^2 d r d t & d r d t = 1 2 r^2 = 1 2 6^2 = 1 72 ~cm / s & aligned [ V=288 = 4 3 r^3 216=r^3 r=6 ]

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