https://file.aiquickdraw.com/mathbot/file/1728760801804fuupy69i.jpg

The problem provides the formula for the volume of a sphere:

\[
V = \frac{4}{3} \pi r^3
\]

We are given that the volume of the bouncy ball is \( 4200\pi \, \text{mm}^3 \), and we need to find the radius \(r\), keeping the answer to 2 decimal places if necessary.

### Step-by-Step Solution:

1. The volume formula is:

\[
V = \frac{4}{3} \pi r^3
\]

2. Substitute the given volume \( V = 4200 \pi \, \text{mm}^3 \) into the formula:

\[
4200 \pi = \frac{4}{3} \pi r^3
\]

3. Divide both sides by \( \pi \) to simplify:

\[
4200 = \frac{4}{3} r^3
\]

4. Multiply both sides by \( \frac{3}{4} \) to isolate \( r^3 \):

\[
r^3 = 4200 \times \frac{3}{4} = 3150
\]

5. Now, take the cube root of both sides to solve for \( r \):

\[
r = \sqrt[3]{3150}
\]

6. Using a calculator to find the cube root:

\[
r \approx 14.72 \, \text{mm}
\]

Thus, the radius of the bouncy ball is approximately \( \boxed{14.72 \, \text{mm}} \).

Would you like more details on any step, or do you have any other questions?

### 5 Related Questions:
1. How is the volume of a cylinder different from that of a sphere?
2. What is the formula for the surface area of a sphere, and how would you apply it here?
3. How would the result change if the volume was given in \( \text{cm}^3 \) instead of \( \text{mm}^3 \)?
4. How would you solve this problem if the sphere was hollow with a certain thickness?
5. What is the relationship between the radius and diameter of a sphere?

### Tip:
When dealing with sphere-related problems, always ensure your units are consistent throughout your calculations.

The bouncy ball below is a sphere with a volume of 4200π mm³. Calculate its radius, r. If your answer is a decimal, give it to 2 d.p.

Learn how to calculate the radius of a sphere given its volume using the formula V = 4/3 π r³. This example involves finding the radius of a bouncy ball with a volume of 4200π mm³, with a final answer rounded to 2 decimal places. Suitable for Grades 8-10.

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