A: Piston cross$-$sectional area $=51024\%$m$25\backslash$times $10^\{-2\}\backslash$pm $4\backslash \%\backslash ,\backslash$text$\{$m$\}^251024\%$m$2$

L$1=0\mathrm{.}55\%$mL$\_1=0\mathrm{.}5\backslash$pm $5\backslash \%\backslash ,\backslash$text$\{$m$\}$L$1=0\mathrm{.}55\%$m

L$2=0\mathrm{.}753\%$mL$\_2=0\mathrm{.}75\backslash$pm $3\backslash \%\backslash ,\backslash$text$\{$m$\}$L$2=0\mathrm{.}753\%$m

KKK: Spring constant $=7\mathrm{.}5103150$N$/$m$7\mathrm{.}5\backslash$times $10^3\backslash$pm $150\backslash ,\backslash$text$\{$N$/$m$\}7\mathrm{.}5103150$N$/$m

$$X$=2\mathrm{.}510\mathrm{.}1$mm$\backslash$Delta X $=2\mathrm{.}5\backslash$pm $10\mathrm{.}1\backslash ,\backslash$text$\{$mm$\}$X$=2\mathrm{.}510\mathrm{.}1$mm

Questions:

a$.$ Determine the relationship between the scale reading and the pressure in the cylinder:

P$=$P$($R$,$L$1,$L$2,$K$,$A$)$P $=$ P$($R$,$ L$\_1,$ L$\_2,$ K$,$ A$)$P$=$P$($R$,$L$1,$L$2,$K$,$A$)$

b$.$ What is the nominal pressure in the piston?

c$.$ Determine the error in measuring the pressure $($PPP$)$ due to the errors listed above.