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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.

Calculate the radius of a sphere given its volume is 4800π mm³.

Learn how to calculate the radius of a sphere when given the volume as 4800π mm³. This problem demonstrates how to apply the volume of a sphere formula V = (4/3)πr³ and simplify the equation. Suitable for students in Grades 8-10.

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