Chapter 13 - Partial Derivatives - 13.4 Differentiability, Differentials, And Local Linearity - Exercises Set 13.4 - Page 948: 54

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The volume of cone with height h , radius $r$, and volume V is given as $\frac{\pi r^{2} h}{3}=V$. Thus: \[ \begin{array}{l} \frac{\pi(2 r h d r)}{3}+\frac{\left(\pi r^{2}\right) d h}{3}=d V \\ \frac{2 d r}{r}+\frac{d h}{h}=\frac{d V}{V} \\ 0.01=\frac{d r}{r} \\ 0.04=\frac{d h}{h} \\ \frac{d V}{V}=0.01 \times 2 +0.04 \\ 0.06=\frac{d V}{V} \end{array} \]