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JEE Main2014MathematicsApplication of DerivativesActual

If the volume of a spherical ball is increasing at the rate of 4 π cc / sec then the rate of increase of its radius in cm / sec , when the volume is 288 π cc is

Options

  1. A1 9
  2. B1 6
  3. C1 2 4
  4. D1 3 6

Correct answer

D. 1 3 6

Step-by-step solution

Volume of sphere of radius r is V = 4 3 π r 3 Given V = 288 π   cc ⇒ 288 π = 4 3 π r 3 ⇒ r 3 = 288 × 3 4 = 216 ⇒ r = 6   cm . Again, V = 4 3 π r 3 Differentiate w.r.t. ' t ' ⇒ d V d t = 4 π r 2 d r d t Put the given values, to get ⇒ 4 π = 4 π × 6 2 × d r d t ⇒ d r d t = 1 3 6   cm / sec .

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