The volume of the cup is : \(\left(\dfrac{6}{2}\right)^2\pi.12=108\pi\) (cm³)

The volume of 48 tapioca bubbles is : \(108\pi-100\pi=8\pi\) (cm³)

The volume of each tapioca bubble is : \(\dfrac{8\pi}{48}=\dfrac{\pi}{6}\) (cm³)

The answer is : \(\sqrt[3]{\dfrac{\pi}{6}:\dfrac{4\pi}{3}}=0.5\) (cm)