# Related Rates Problem

• Nov 12th 2006, 12:36 PM
Affinity
Related Rates Problem
The volume V of a spherical cancer tumor is given by , where x is the diameter of the tumor. It is estimated that the diameter of the tumor is growing at a rate of 0.4 millimeters per day, at the point in time where the diameter is already 10 millimeters. How fast is the volume of the tumor increasing at this time? (Thanks in advance!)
• Nov 12th 2006, 12:52 PM
topsquark
Quote:

Originally Posted by Affinity
The volume V of a spherical cancer tumor is given by http://img.photobucket.com/albums/v3...mnleafs/11.jpg, where x is the diameter of the tumor. It is estimated that the diameter of the tumor is growing at a rate of 0.4 millimeters per day, at the point in time where the diameter is already 10 millimeters. How fast is the volume of the tumor increasing at this time? (Thanks in advance!)

$\displaystyle V = \frac{ \pi x^3}{6}$

Thus $\displaystyle dV = \frac{ \pi}{6} \cdot 3x^2 dx$

Use $\displaystyle dx \approx 0.4 \, mm/day$. Then $\displaystyle dV \approx 62.832 \, mm^3/day$

-Dan