Thread: differential equation for a sphere

The rate of change of volume of a sphere is proportional to the volume of the sphere. Obtain a differential equation for the radius.


I am keep getting kr/3 when the answer they gave in the textbook its from is 4kr please help for dr/dt

Originally Posted by righteous818

The rate of change of volume of a sphere is proportional to the volume of the sphere. Obtain a differential equation for the radius.


I am keep getting kr/3 when the answer they gave in the textbook its from is 4kr please help for dr/dt

What you have written makes no sense. The question appears to be "Obtain a differential equation for the radius" but neither what you give as your answer, "kr/3", nor the answer you say is in the book "4kr", is a differential equation.

Perhaps if you show what you have done to arrive at "kr/3" as a "differential equation" we could help.

i meant that they want dr/dt, i got dr/dt= kr/3 while the book's answer is dr/dt= 4kr

what i did is used chain rule

dv/dt=dv/dr x dr/dt

then dv/dt is proportional to v so
dv/dt=k(4/3 x pi x r^3)

then
dr/dt= (dv/dt)/(dv/dr)
= (k(4/3 x pi x r^3))/(4x pi x r^2)
= kr/3

but the answer they have is dr/dt= 4kr

it could mean that the factor of 12 is incorporated into the constant k so that r'=4kr, where k2=k1/12