The given equation represents the volume $V_s$ of a sphere:

$V_s = \frac{4}{3} \pi r^3 = 12.8 \, \text{cm}^3$

We need to solve for $r$, the radius of the sphere.

Step 1: Start with the equation for the volume:

$\frac{4}{3} \pi r^3 = 12.8$

Step 2: Isolate $r^3$:

Multiply both sides by $\frac{3}{4 \pi}$ to isolate $r^3$: $r^3 = \frac{3 \cdot 12.8}{4 \pi}$

Step 3: Calculate $r^3$:

$r^3 = \frac{3 \cdot 12.8}{4 \cdot 3.1416} = \frac{38.4}{12.5664} \approx 3.056$

Step 4: Solve for $r$:

Take the cube root of both sides: $r = \sqrt[3]{3.056} \approx 1.45 \, \text{cm}$

So, the radius $r \approx 1.45 \, \text{cm}$.

Would you like more details on this process or have any questions?

Here are five related questions for further exploration:

1. What is the surface area of the sphere with this radius?
2. How does the volume of a sphere change as the radius increases?
3. If the volume was doubled, what would the new radius be?
4. Can you calculate the diameter of the sphere?
5. How would the volume change if the radius was increased by 50%?

Tip: To quickly calculate the volume of a sphere, remember the formula $V = \frac{4}{3} \pi r^3$, where the volume is proportional to the cube of the radius.