$4-2$ Use your data to calculate the volume of the cylinder. Propagate the uncertainty of your measurements for this calculation. Give your result with both the absolute and relative uncertainty. Be sure it is clear to the reader what you are doing and why.

$4-3$ Use your data to calculate the mass density of the cylinder. The mass density is the mass divided by the volume. Be careful with units! Propagate the uncertainty of your measurements for this calculation using the more advanced $($standard$)$ method. Give your result with both the absolute and relative uncertainty. Be sure it is clear to the reader what you are doing and why.

Diameter $1\mathrm{.}74cm+-0\mathrm{.}01cm$

length $6\mathrm{.}21cm+-0\mathrm{.}01cm$

Mass $42\mathrm{.}4g+-0\mathrm{.}1g$

$P_{cyL}=\frac{m}{\sqrt[\phantom{2}]{CyL}}=\frac{m}{(\frac{}{4}{D}^{2}L)}=\frac{4m^1}{D^{2}L}$

$r_{{}_{CVL}}=\sqrt[\phantom{2}]{(1*r_m{)}^2+(2*r_D{)}^2+(1+r_L{)}^2}$

$=\sqrt[\phantom{2}]{(1*\frac{9m}{m}{)}^2+(2*\frac{9D}{D}{)}^2+(1*\frac{9L}{L}{)}^2}$

$a{P}_{CYLL}=(r_{CYLL})(P_{CYL})$

absolute UNC.

of a calculated value

Add$/$sub case meavured$)$

Mult$/$Div Case

"absolute" uncertainty of a value, $v,$ is denoted By $a_v$ "relative" uncertainty of a value, $v,$ is denoted by $f_v$

AND,$r_v=\frac{a_v}{v}$

OR

$r_v\%=(\frac{\frac{?}{abs}\text{u}\text{n}\text{c}}{\text{m}\text{e}\text{a}\text{s}\text{i}\text{c}\text{d}\text{v}\text{a}\text{l}\text{u}\text{e}})100\%$