To solve this problem, we need to calculate the volume $V$ of a sphere using the given diameter $D = 8.6 \, \text{cm}$.

Step-by-Step Solution

1. Formula for the Volume of a Sphere: $V = \frac{4}{3} \pi r^3$ where $r$ is the radius of the sphere.

2. Calculate the Radius: Since the diameter $D$ is given, we can find the radius $r$ by dividing the diameter by 2: $r = \frac{D}{2} = \frac{8.6 \, \text{cm}}{2} = 4.3 \, \text{cm}$

3. Substitute Values into the Volume Formula: Using $\pi \approx 3.14$: $V = \frac{4}{3} \times 3.14 \times (4.3)^3$

4. Calculate $4.3^3$: $4.3^3 = 4.3 \times 4.3 \times 4.3 = 79.507$

5. Calculate the Volume: Substitute $79.507$ for $r^3$: $V = \frac{4}{3} \times 3.14 \times 79.507$ $V \approx \frac{4}{3} \times 249.69698$ $V \approx 332.9293 \, \text{cm}^3$

6. Round to the Nearest Tenth: $V \approx 332.9 \, \text{cm}^3$

Final Answer

The volume of the sphere is approximately: $V = 332.9 \, \text{cm}^3$

Would you like further details or have any questions?

Here are some related questions that might expand your understanding:

1. What would the volume be if the diameter were doubled?
2. How does the formula for the surface area of a sphere compare to the volume formula?
3. What happens to the volume if the radius is halved?
4. Can the volume formula be derived from basic calculus concepts?
5. How does the value of $\pi$ affect the final volume result?

Tip: Remember, for spheres, the volume increases with the cube of the radius, meaning small changes in radius can significantly impact the volume.