To find the volume of the sphere, we use the formula:

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

where:

• $\pi \approx 3.14$
• $r = 10 \, \text{mm}$

Step-by-Step Solution:

1. Cube the Radius: $r^3 = 10^3 = 1000$

2. Multiply by $\pi$: $\pi r^3 = 3.14 \times 1000 = 3140$

3. Multiply by $\frac{4}{3}$: $V = \frac{4}{3} \times 3140 = 4186.67$

So, the volume of the sphere is approximately 4186.67 cubic millimeters.

Would you like further details or explanations on this problem?

Here are some related questions to consider:

1. What is the formula for the surface area of a sphere?
2. How does the volume change if the radius doubles?
3. Can you calculate the volume using a more precise value of $\pi$?
4. What is the relationship between radius and volume in a sphere?
5. How would you solve for the radius if the volume is given?

Tip: Remember that for spheres, small changes in radius result in significant volume changes because of the $r^3$ relationship in the formula.