Answer to Question #278285 in Physics for Zendaya

Question

The diameter d, of a wire is (0.56m 0.01mm) if it's cross sectional area A is given by m², calculate the following; I)The maximum fractional uncertainty in A (ii) maximum uncertainty in A (iii) cross sectional area of the wire.

Answer 1

$$\frac{\Delta A}{A}=2\frac{(10^{-5})}{0.56}=3.6\cdot10^{-5}\\ \Delta A=3.6\cdot10^{-5}(0.246)=8.9\ mm^2\\A=0.25\pi(0.56)^2=0.246\ m^2$$