Use textbook chapter $6,$ problem $16$ as a context reference, but follow these instructions:

Note that both Python Math and Excel have intrinsic functions for the arc$-$cosine $(co{s}^{-1}(x)).$

a$.$ Use a combination of the graphical and bisection methods in an Excel worksheet to find $h$ for $r=2m,L=5m$ and $V=8m^3.$

b$.$ Use a combination of the graphical and Newton$-$Raphson iteration methods in Python to find $h$ for $r=2m,L=5m$ and $V=36m^3$

c$.$ Use a combination of the graphical and secant methods in either Excel or Python $($your choice$)$ to find $h$ for $r=2m,L=5m$ and $V=52m^3$

d$.$ Use the Python fsolve to find $h$ for $r=3m,L=6m$ and $V=52m^3.$

e$.$ Use the Excel solver to find $h$ for $r=3m,L=6m$ and $V=47m^3.$

$6\mathrm{.}16$ The volume of a liquid, $V,$ in a horizontal, cylindrical tank of radius, $R,$ and length, $L,$ is given by the formula

$V=[R^{2}co{s}^{-1}(\frac{R-h}{R})-(R-h)\sqrt[\phantom{2}]{2Rh-h^2}]L$

where $h=$ the depth of the liquid at the centerline of the cylinder.

$($a$)$ Determine $h,$ given $R=2m,L=5m,$ and $V=8m^3.$