Fix this code and theres a error and use the equation in the picture :Oblate spheroid calculations.

An oblate spheroid such as the Earth is obtained by revolving an ellipse about its minor axis.In everyday terms, it is the

shape of a slightly compressed beach ball. The Earth's equatorial radius is about

$2$

$0$

$$km longer than its polar radius. The

surface area of an oblate spheroid is given by:Oblate spheroid calculations.

An oblate spheroid such as the Earth is obtained by revolving an ellipse about its minor axis. In everyday terms, it is the

shape of a slightly compressed beach ball. The Earth's equatorial radius is about $20$ km longer than its polar radius. The

surface area of an oblate spheroid is given by:

$A(r_1,r_2)=2(r_1^2+\frac{r_2^2}{sin()}ln(\frac{cos()}{1-sin()}))$

where r $1$ is the equatorial radius, r $2$ is the polar radius, and $=arccos(\frac{r_2}{r_1}).$

Write a script that prompts the user to inputs the equatorial and polar radii. If the radii follow the rule $A(r_1$;$r_2)A_{\text{a}\text{p}\text{p}\text{r}\text{o}\text{x}}=4(\frac{r_1+r_2}{2}{)}^2(r_1$;$r_2)=(6378\mathrm{.}137,6356\mathrm{.}752)r2,$ then

calculate and display both $A(r_1$;$r_2)$ and the approximation $A_{\text{a}\text{p}\text{p}\text{r}\text{o}\text{x}}=4(\frac{r_1+r_2}{2}{)}^2.$ Apply the script $to$ the Earth

data $(r_1$;$r_2)=(6378\mathrm{.}137,6356\mathrm{.}752).$ Display $6$ significant figures per answer $to$ reveal the discrepancy.$\%$ Sarah$\_005\_$HW$\_60\_$main.m

$\%$ MATLAB script to calculate the surface area of an oblate spheroid

$\%$ Prompt user for input

r$1=$ input$(\text{'}$Enter the equatorial radius $($r$1)$ in km: $\text{'})$;

r$2=$ input$(\text{'}$Enter the polar radius $($r$2)$ in km: $\text{'})$;

$\%$ Check if the input radii follow the rule r$2$ r$1$

if r$2>=$ r$1$

error$(\text{'}$Error: Polar radius $($r$2)$ must be less than the equatorial radius $($r$1).\text{'})$;

end

$\%$ Calculate the approximate surface area using A$\_$approximation

A$\_$approx $=4*$ pi $*(($r$1^2+$ r$2^2)/2)$;

$\%$ Display the results with $6$ significant figures

fprintf$(\text{'}$Surface area A$($r$1,$ r$2)=\%\mathrm{.}6$f km$^2$

$\text{'},$ A$)$;

fprintf$(\text{'}$Approximate surface area A$\_$approx $=\%\mathrm{.}6$f km$^2$

$\text{'},$ A$\_$approx$)$;

$\%$ Apply the script to the Earth data $($r$1,$ r$2)=(6378\mathrm{.}137,6356\mathrm{.}752)$

fprintf$(\text{'}$

Applying to Earth data $($r$1=6378\mathrm{.}137,$ r$2=6356\mathrm{.}752)$:

$\text{'})$;

r$1\_$earth $=6378\mathrm{.}137$; $\%$ Equatorial radius in km

r$2\_$earth $=6356\mathrm{.}752$; $\%$ Polar radius in km

$\%$ Calculate the eccentricity e for Earth data

e$\_$earth $=$ sqrt$(1-($r$2\_$earth$^2/$ r$1\_$earth$^2))$;

$\%$ Calculate the surface area A$($r$1,$ r$2)$ for Earth data

A$\_$earth $=2*$ pi $*$ r$1\_$earth$^2*(1+((1-$ e$\_$earth$^2)/$ e$\_$earth$)*$ atan$($e$\_$earth$))$;

$\%$ Calculate the approximate surface area using A$\_$approximation for Earth data

A$\_$approx$\_$earth $=4*$ pi $*(($r$1\_$earth$^2+$ r$2\_$earth$^2)/2)$;

$\%$ Display the results for Earth data with $6$ significant figures

fprintf$(\text{'}$Surface area A$($r$1,$ r$2)$ for Earth $=\%\mathrm{.}6$f km$^2$

$\text{'},$ A$\_$earth$)$;

fprintf$(\text{'}$Approximate surface area A$\_$approx for Earth $=\%\mathrm{.}6$f km$^2$

$\text{'},$ A$\_$approx$\_$earth$)$;