Derivatives - find the rate at which the diameter is increasing when the diameter is 20cm

Question

A spherical balloon is being inflated so that its volume is increasing at the rate of 10cm³/sec. Find the rate at which the diameter is increasing when the diameter is 20cm.

Answer 1

V = 4/3*pi*"R^3

 

   = 4/3  * pi * (1/2*D)^3

 

   = 4/3 * pi * 1/8 * D^3

 

  = 1/6 * pi * D^3

 

 

dV/dt = 1/6 * pi * 3 * D^2 * dD/dt

 

           = 1/2*pi * D^2 * dD/dt

 

 

    10       = 1/2*pi*20^2 * dD/dt

 

   10 = 1/2*pi*400 * dD/dt

 

 20 = pi * 400 * dD/dt

 

 1/20 = pi * dD/dt

 

 1/(20*pi) = dD/dt