It seems like the volume equation for the cantaloupe is incomplete in your query. However, I assume the volume is modeled as a sphere, so the volume formula would likely be:

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

Where:

• $V$ is the volume,
• $r$ is the radius of the cantaloupe,
• and $\pi$ is a constant.

We are given that the radius is increasing at a rate of $\frac{dr}{dt} = 0.2 \, \text{cm/week}$, and at the moment of interest, the radius $r = 8.6 \, \text{cm}$.

To find how fast the volume is changing at that moment, we need to compute the rate of change of the volume $\frac{dV}{dt}$. We can do this using related rates.

Step 1: Differentiate the volume equation

We begin by differentiating the volume formula with respect to time $t$ using the