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AP EAMCET202120 Aug 2021Evening ShiftMathematicsApplication of DerivativesActual

The volume of a spherical balloon is increasing at the rate of 30 cc per minute. Find the rate of change of surface area of the balloon, when its radius is 6 cm .

Options

  1. A5   cm 2 · min - 1
  2. B30   cm 2 · min - 1
  3. C10   cm 2 · min - 1
  4. D20   cm 2 · min - 1

Correct answer

C. 10   cm 2 · min - 1

Step-by-step solution

⇒ v = volume of sphere of radius   r ⇒ v = 4 3 π   r 3 ⇒ d v d t = 30   c c / m i n ⇒ d d t 4 3 π   r 3 = 30 ⇒ 4 3 π   3   r 2 dr dt = 30 ⇒ d r d t = 30 4 π   r 2             1 ⇒ s = surface area of balloon   ⇒ s = 4 π   r 2 ⇒rate of change of surface area of the balloon = d s d t ⇒ d

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