# Math Help - Relative rates of change.

1. ## Relative rates of change.

I'm stuck on this problem: ( u = mu, since I don't know how to do the symbol)

"A spherical cell is growing at a constant rate of 400 um^3/day (1 um = 10^-6 m). At what rate is its radius increasing when the radius is 10 um?"

If someone could help me set this problem up, I'd appreciate it! Thanks!

2. By the Chain Rule, we know that

$\frac{dV}{dt}=\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)=4\pi r^2\frac{dr}{dt}=400.$