Area and Circumference of a Circle Study the program below, which uses both variables and constants: $//************************************************************//$ Circle.java $////$ Print the area of a circle with two different radii $//************************************************************$ public class Circle $\{$ public static void main$($String$[]$ args$)\{$ final double PI $=3\mathrm{.}14159$; int radius $=10$; double area $=$ PI $*$ radius $*$ radius; System.out.println$("$The area of a circle with radius $"+$ radius $+"$ is $"+$ area$)$; radius $=20$; area $=$ PI $*$ radius $*$ radius; System.out.println$("$The area of a circle with radius $"+$ radius $+"$ is $"+$ area$)$; $\}\}$ Some things to notice: The first three lines inside main are declarations for PI$,$ radius, and area. Note that the type for each is given in these lines: final double for PI$,$ since it is a floating point constant; int for radius, since it is an integer variable, and double for area, since it will hold the product of the radius and PI$,$ resulting in a floating point value. These first three lines also hold initializations for PI$,$ radius, and area. These could have been done separately, but it is often convenient to assign an initial value when a variable is declared. The next line is simply a print statement that shows the area for a circle of a given radius. The next line is an assignment statement, giving variable radius the value $20.$ Note that this is not a declaration, so the int that was in the previous radius line does not appear here. The same memory location that used to hold the value $10$ now holds the value $20$we are not setting up a new memory location. Similar for the next line$$no double because area was already declared. The final print statement prints the newly computed area of the circle with the new radius. Save this program, which is in file Circle.java, into your directory and modify it as follows: $1.$ The circumference of a circle is two times the product of Pi and the radius. Add statements to this program so that it computes the circumference in addition to the area for both circles. You will need to do the following: Declare a new variable to store the circumference. Store the circumference in that variable each time you compute it$.$ Add two additional print statements to print your results. Be sure your results are clearly labeled. $2.$ When the radius of a circle doubles, what happens to its circumference and area? Do they double as well? You can determine this by dividing the second area by the first area. Unfortunately, as it is now the program overwrites the first Chapter $2$: Data and Expressions $17$ area with the second area $($same for the circumference$).$ You need to save the first area and circumference you compute instead of overwriting them with the second set of computations. So you'll need two area variables and two circumference variables, which means they'll have to have different names $($e$.$g$.,$ area$1$ and area$2).$ Remember that each variable will have to be declared. Modify the program as follows: Change the names of the area and circumference variables so that they are different in the first and second calculations. Be sure that you print out whatever you just computed. At the end of the program, compute the area change by dividing the second area by the first area. This gives you the factor by which the area grew. Store this value in an appropriately named variable $($which you will have to declare$).$ Add a println statement to print the change in area that you just computed. Now repeat the last two steps for the circumference. Look at the results. Is this what you expected? $3.$ In the program above, you showed what happened to the circumference and area of a circle when the radius went from $10$ to $20.$ Does the same thing happen whenever the radius doubles, or were those answers just for those particular values? To figure this out, you can write a program that reads in values for the radius from the user instead of having it