# Need help with related rates

• Dec 6th 2006, 08:03 PM
Sky12
Need help with related rates
Im trying to understand related rates here and im getting stuck at this word problem.

It says if V is the volume of a sphere with radius r, and the volume of the sphere decreases as the time passes. express dV/dt in terms of dr/dt. Describe the relationship in words.

I dont get what it means by dV/dt in terms of dr/dt, i know what the derivatives and related rates mean, but I have trouble connecting them to each other.
• Dec 6th 2006, 09:06 PM
CaptainBlack
Quote:

Originally Posted by Sky12
Im trying to understand related rates here and im getting stuck at this word problem.

It says if V is the volume of a sphere with radius r, and the volume of the sphere decreases as the time passes. express dV/dt in terms of dr/dt. Describe the relationship in words.

I dont get what it means by dV/dt in terms of dr/dt, i know what the derivatives and related rates mean, but I have trouble connecting them to each other.

Volume of sphere:

$\displaystyle V=\frac{4}{3}\,\pi\,r^3$

so:

$\displaystyle \frac{dV}{dt}=\frac{d}{dt}\left(\frac{4}{3}\,\pi\, r^3\right)=\frac{4}{3}\,\pi\,\frac{d}{dt}r^3=\frac {4}{3}\,\pi\,3\,r^2\, \frac{dr}{dt}=4\,\pi\,r^2\, \frac{dr}{dt}$

RonL