1. ## 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!)

2. Originally Posted by Affinity
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!)
$V = \frac{ \pi x^3}{6}$

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

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

-Dan