Step 1 :We are given the volume of the sphere and we need to find the radius. We can use the formula for the volume of a sphere, which is \(\frac{4}{3} \pi r^{3}\), and solve for r.
Step 2 :We can do this by first multiplying both sides of the equation by \(\frac{3}{4\pi}\) to isolate \(r^{3}\).
Step 3 :\(r^{3} = \frac{3V}{4\pi} = \frac{3 \times 4800\pi}{4\pi} = 3600\)
Step 4 :Then, we take the cube root of both sides to solve for r.
Step 5 :\(r = \sqrt[3]{3600} = 15.33\)
Step 6 :Final Answer: The radius of the sphere is \(\boxed{15.33}\) mm.