In this exercise you will calculate various mathematical properties of
oblate spheroids – flattened spheres whose shape is defined by
their **equatorial radius** \(a\) and **polar radius** \(c\). Planets
such as the Earth or Saturn are typically modelled as having such a shape.

Start by creating a directory for this exercise. In that directory, create
a file named `Spheroid.java`

. Define a class named `Spheroid`

in this file,
and put your program in this class.

Your program should prompt the user to enter values for the equatorial and
polar radii \(a\) and \(c\) of an oblate spheroid, in units of kilometres.
Use the `Scanner`

class to obtain these values, storing them as `double`

variables. **Do not do any error checking on these values.**

Your program should compute the **eccentricity** of the spheroid, given
by the formula

$$e = \sqrt{1 - \frac{c^{2}}{a^{2}}}$$

Your program should also compute the **volume** of the spheroid, using the
formula

$$V = \frac{4\pi a^{2} c}{3}$$

Finally, your program should display two lines of output, one showing the
eccentricity of the spheroid, the other showing its volume. Use
`System.out.printf()`

to generate both lines of output. Eccentricity
should be displayed to 3 decimal places. For the display of volume, use
`%g`

as the formatting directive. See Section 2.4.1 of Eck’s book
if you need further help with formatted printing.

Here is an example of what the user should see when running the program from a terminal window:

```
$ java Spheroid
Enter equatorial radius in km: 6378.1
Enter polar radius in km: 6356.8
Eccentricity = 0.082
Volume = 1.08320e+12 cubic km
```

The example above uses radii for Earth. Here’s another example, using radii for Saturn:

```
$ java Spheroid
Enter equatorial radius in km: 60268
Enter polar radius in km: 54364
Eccentricity = 0.432
Volume = 8.27130e+14 cubic km
```

(Here the higher eccentricity indicates that Saturn is significantly more ‘squashed’ than the Earth, due to a much higher speed of rotation.)

- You can use the built-in constant
`Math.PI`

for the value of \(\pi\) - You can use the
`Math.sqrt()`

method to compute a square root – see the API documentation for further information - You do not need an import statement to use things defined in the
`Math`

class!

□