sphere increasing in volume at rate of 3(pi)cm^3/s. what rate is its radius changing when the radius is 1/2cm? The volume of a sphere is given as V= 4/3(pi)r^3.

Question

A sphere is increasing in volume at a rate of 3(pi)cm^3/s. At what rate is its radius changing when the radius is 1/2cm? The volume of a sphere is given as V= 4/3(pi)r^3.

Answer 1

Let V = volume of sphere at time t

      r = radius of sphere at time t

 

Given:  dV/dt = 3π

Find:    dr/dt when r = 1/2

 

Solution:  V = (4/3)πr³

 

               dV/dt = (4/3)(3πr²)(dr/dt)

 

                    3π = 4π(1/2)²(dr/dt)

 

                    3π = π(dr/dt)

 

So, dr/dt = 3 cm/sec