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AP EAMCET2003MathematicsApplication of Derivatives

Gas is being pumed into a spherical balloon at the rate of 30 ft ^3 / min . The rate at which the radius increase when it reaches the value 15 ft , is :

Options

  1. A1 30 ft / min
  2. B1 15 ft / min
  3. C1 20 ft / min
  4. D1 25 ft / min

Correct answer

A. 1 30 ft / min

Step-by-step solution

Given that, d V d t =30 ft ^3 / min , r=15 ft Volume of sphere, V= 4 3 r^3 d V d t =4 r^2 d r d t 30=4 (15)^2 d r d t d r d t = 1 30 ft / min

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