A cube is being manufactured with a side length of 96 cm and a maximum possible error of 0.076 cm for the sides. Find the approximate error and the approximate relative error in the volume of the cube. Give the relative error as a percent.

The differential is $LaTeX: \displaystyle dV = 3 s^{2}$ . Evaluating at $LaTeX: \displaystyle s = 96$ and $LaTeX: \displaystyle ds = 0.076$ gives $LaTeX: \displaystyle 2101.248$ . The relative error is given by $LaTeX: \displaystyle \frac{dV}{V} = \frac{3 s^{2}}{s^{3}}\,ds=\frac{3}{s}\,ds$ . Evaluating gives $LaTeX: \displaystyle 0.00238 = 0.238$ %