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MHT CET202519 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the rate of 2.1 ~cm / sec . Then the rate of increase of the enclosed circular region, when the radius of the circular wave is 10 cm, is (Given = 22 7 )

Options

  1. A66 ~cm ^2 / second
  2. B122 ~cm ^2 / second
  3. C132 ~cm ^2 / second
  4. D110 ~cm ^2 / second

Correct answer

C. 132 ~cm ^2 / second

Step-by-step solution

Differentiating the area formula A = r^2 with respect to time using the chain rule gives the relation dA dt = 2 r dr dt . Substituting the given values r = 10 cm , dr dt = 2.1 cm/s , and using = 22 7 yields: dA dt = 2 22 7 10 2.1 = 2 22 7 10 21 10 . Simplifying the expression by canceling the factor of 10 and evaluating 21 7 gives: dA dt = 2 22 3 = 132 . The area increases at a rate of 132 cm ^2/ s when the radius is 10 cm. C

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