Chapter 14 - Partial Derivatives - 14.4 Tangent Planes and Linear Approximations - 14.4 Exercises - Page 975: 35

$16 cm^3$

Volume, $V=\pi r^2 h$ Write the differential form such as follows: $dV=\dfrac{\partial V}{\partial r} \times dr + \dfrac{\partial V}{\partial h} \times dh$ $dV=[ 2 \pi r h] \times dr+[ \pi r^2] \times dh$ $dV=(96 \pi) \times (0.04) +(16 \pi) (0.08) \approx 16 cm^3$