The volume of a horizontal cylindrical tank filled with a fluid is to be estimated using a dipstick. The filled area $A$ of a circle bound by a horizontal chord $($the top of the fluid$)$ is given by

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

where $h$ is the sagitta $($which is the height of the fluid$)$ and $R$ is the radius of the cylinder.

Using MATLAB, produce a chart showing the relationship between fluid depth and actual volume.

Use:

diameter $=9\mathrm{.}1$ m ;

$$ylinder axial length $=4\mathrm{.}7m$

Use Online calculator: Circular segment $($

planetcalc.com$)$ to validate your result and include a minimum of four datapoints from this validation on your chart.