# Volume of a sphere...

• Oct 9th 2007, 02:23 PM
Esiuol
Volume 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, 02:25 PM
Jhevon
Quote:

Originally Posted by Esiuol
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???

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)

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