Welcome to CSC200 Lab 5

Write a C++ program that prompts the user to enter the percentage of the moon's face that appear's illustrated, and outputs the the surface area of that portion of the moon. The formula for the surface area of a segment is
\begin{displaymath}S=2R^2\theta\end{displaymath}

where $R$ is the raduis of the sphere (the moon's raduis is $R=1738.3$km) and $\theta$ is angle of the wedge in radians. There are $2\pi$ radians in a circle so the hemisphere we see accounts for at most $\pi$ radians. Thus, if the user enters 100% (full moon), the angle of the wedge is $\pi$ and the formula is

\begin{displaymath}S=2\cdot 1738.3^2\cdot 3.14159 = 18985818.672.\end{displaymath}

If the user enters 50%, the angle of the wedge is

\begin{displaymath}\pi\cdot 0.5\end{displaymath}

and so on. Use doubles for your calculation and limit the decimal precision to 5 places. You will need the cmath, iostream and iomanip header files.