Question

Suppose the radius is measured to be r=6.0cm+-0.1cm

a,the true value of the radius lies between _

b,what is the significant figure of area

Answer 1

a. $5.9\le r\le6.1\ cm$

b. $A=\pi r^2=3.14\cdot6.0^2=113.0\ (m^2)$

$\frac{\Delta A}{A}=\frac{2\Delta r}{r}\to \Delta =A\cdot\frac{2\Delta r}{r}=113.0\cdot\frac{2\cdot0.1}{6.0}=3.8\ (m^2)$

$A=(113.0\pm3.8)\ m^2$