Why is the rate of change of the volume of a sphere not constant when the rate of change in its radius with respect to time is???

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- Oct 9th 2007, 01:23 PMEsiuolVolume of a sphere...
Why is the rate of change of the volume of a sphere not constant when the rate of change in its radius with respect to time is???

- Oct 9th 2007, 01:25 PMJhevon
because the rate of change of the volume does not only depend on the rate of change of the radius but also the radius itself (which is changing)

$\displaystyle \frac {dV}{dt} = 4 \pi r^2~\frac {dr}{dt}$ ..........if $\displaystyle \frac {dr}{dt} \ne 0$, then $\displaystyle r$ is changing and is therefore a variable, which makes $\displaystyle dV/dt$ a dependent variable