The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$. The constants $\frac{4}{3}$ and $\pi$ are exact and do not contribute to the error. For a quantity $X = r^p$, the fractional error is $\frac{\Delta X}{X} = p\frac{\Delta r}{r}$. In this case, for $V = r^3$, the fractional error in volume is $\frac{\Delta V}{V} = 3\frac{\Delta r}{r}$. Given radius $r = 2.0 \text{ cm}$ and absolute error $\Delta r = 0.1 \text{ cm}$. Fractional error in radius $\frac{\Delta r}{r} = \frac{0.1}{2.0} = 0.05$. Now, calculate the fractional error in volume: $\frac{\Delta V}{V} = 3 \times 0.05 = 0.15$. To convert this to percentage error, multiply by $100\%$: Percentage error in volume $= 0.15 \times 100\% = 15\%$.