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From the picture we know that the diameter of the sphere is equal to the height and "width" of the cylinder. We know that a sphere's volume is \(\frac{4}{3}\pi r^3\) where \(r\) is the radius. We also know that the cylinder's volume is \(\pi r^2 h\) where \(r\) is the radius and \(h\) is the height. But as we said before (because the sphere is inscribed within the cylinder) that the height and "width" (diameter) is the same so we can rewrite that to \(2\pi r^3\). The ratio of it is \(\frac{\frac{4}{3}\pi r^3}{2\pi r^3}\). \(\pi r^3\) cancels out and we are left with \(\frac{\frac{4}{3}}{2}\) simplify that to \(\Rightarrow\) \(\frac{4}{2\times3} \Rightarrow \frac {4}{6}\) . We can simplify that further to \(\frac{2}{3}\) because both are divisible by 2. So the answer is \(\boxed{\frac{2}{3}}\) or \(\boxed{2:3}\)