The formula for the volume of a sphere is given as:

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

We are provided with the volume $V = 4800\pi \ \text{mm}^3$. To find the radius $r$, we need to solve for $r$ from the volume formula:

$4800\pi = \frac{4}{3} \pi r^3$

We can simplify by canceling $\pi$ from both sides:

$4800 = \frac{4}{3} r^3$

Next, solve for $r^3$:

$r^3 = \frac{4800 \times 3}{4} = 3600$

Now, take the cube root of both sides to find $r$:

$r = \sqrt[3]{3600}$

Let me calculate this for you.The radius $r$ of the sphere is approximately 15.33 mm, rounded to two decimal places.

Would you like more details or have any questions? Here are some related questions:

1. How is the volume of a sphere formula derived?
2. What is the significance of the $\pi$ symbol in this equation?
3. How do you convert the volume if it was given in different units, like cm³ instead of mm³?
4. Can this formula be applied to non-spherical objects?
5. How would the calculation change if the volume was given without $\pi$?

Tip: Always simplify equations by canceling out common terms like $\pi$ to make solving easier.