A cube is being manufactured with a side length of 43 cm and a maximum possible error of 0.029 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 $LaTeX: \displaystyle s = 43$ and $LaTeX: \displaystyle ds = 0.029$ gives $LaTeX: \displaystyle 160.863$ . The relative error is given by $LaTeX: \displaystyle \frac{dV}{V} = \frac{3 s^{2}}{s^{3}}\,ds=\frac{3}{s}\,ds$ . Evaluating gives $LaTeX: \displaystyle 0.00202 = 0.202$ %