Script Files

Area and Volume of an Oblate Spheroid

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 $6378\mathrm{.}137$ km$,$ and its polar radius is $6356\mathrm{.}752$ km$.$

The volume of an oblate spheroid is given by the formula

V $=4$

$3\backslash$pi r$2$

e rp$,$

and its surface area is given by the formula

A $=2\backslash$pi r$2$

e $+$ r$2$

p

sin$(\backslash$gamma $)$ ln

cos$(\backslash$gamma $)$

$1$ sin$(\backslash$gamma $)$

$!$

$,(1)$

where re represents the equatorial radius; rp represents the polar radius; and

$\backslash$gamma $=$ arccos

rp

re

$.$

Write the R script file oblate.r that prompts the user for two inputs: re and rp and

prints the volume and the surface area of the oblate spheroid determined by re and rp$.$

This will take two of R$$s as$.$numeric$($readline$())$ statements, one for re and one for

rp$,$ and you will need to use several of R$$s built$-$in functions: sin$,$ cos$,$ log$,$ and acos.

These represent the sine$,$ cosine, natural logarithm $($log base e$),$ and arccosine functions,

respectively.

The inputs for all the trigonometric functions in R are in radians. So$,$ for instance, the

R command

$>$ sin$($pi$/2)$

means that you are taking the sine of $\backslash$pi $/2$ radians $($or $90$ degrees!$).$ The cos$,$ log$,$ and

acos are similar. In the formula, $$ln$$ means the $$natural logarithm$$ or $$log base e$.$ In

R$,$ use the command log$.$ So$,$ the R command

$>$ log$(1000)$

means ln$(1000).$

Error Checking

Note that re should be greater than or equal to rp$.$ If the user inputs values of re and rp

such that re $<$ rp$,$ print an error message, and stop execution of the script file. Also, note