Chapter 3: Derivatives - Section 3.9 - Linearization and Differentials - Exercises 3.9 - Page 175: 50

$1\%$

Step 1. Volume $V=\frac{\pi D^3}{6}$ where $D$ is the diameter. We have $dV=\frac{\pi D^2dD}{2}$ and $\frac{dV}{V}=\frac{\frac{\pi D^2dD}{2}}{\frac{\pi D^3}{6}}=\frac{3dD}{D}$ Step 2. We need $\frac{dV}{V}\leq3\%$ that is $\frac{3dD}{D}\leq3\%$ or $\frac{dD}{D}\leq1\%$