air is being pumped into spherical balloon at a rate of 4.5 cubic feet per minute. find the rate of change of the radius when the radius is 2 feet

Question

Pls give me the answer and solvings pls thank u

Answer 1

Let V = volume (in ft ³ ) of the balloon in t minutes

 

      r = radius (in ft) of the balloon after t minutes

 

Given:  dV/dt = 4.5  Find:  dr/dt when r = 2

 

V = (4/3)πr³

 

So, dV/dt = 4πr²(dr/dt) 

 

     4.5 = 4π(2)²(dr/dt)

 

     dr/dt = 9/(32π) ft/min