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

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- Dec 19th 2012, 09:05 AMrighteous818differential 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 - Dec 19th 2012, 11:46 AMHallsofIvyRe: differential equation for a sphere
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. - Dec 19th 2012, 11:56 AMrighteous818Re: differential equation for a sphere
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 - May 12th 2013, 10:46 AMmathnerd15Re: differential equation for a sphere
it could mean that the factor of 12 is incorporated into the constant k so that r'=4kr, where k2=k1/12