1. ( 20 points ) The given curve is rovolved about the x-axis or y-axis. Find the area and volume of the resulted surface and object.
   1. y = √(4 - x²)         -1 ≤ x ≤ 1     ( about x-axis )
   2. x = √(a² - y²)         0 ≤ y ≤ a/2     ( about y-axis )

   Write a program that generates the surfaces from the curves ( assume any value of a you prefer ).

2. ( 10 points ) Search the Internet to download a .3ds file. Render the 3ds object; customize your display with your own lighting effect, camera view and rotation.

3. (10 points ) Write a program that generates a double-headed arrow prism. ( In the class, we have discussed a single-headed arrow prism. )

4. ( 20 points ) Find a Frenet frame for the hyperbola given by x(t) = sec ( t )
   y(t) = tan ( t )
   z(t) = t Write a program that generates a tube using the above hyperbola.

   Extra Credit ( 15 points ) Use blender to create a 3-D chess piece. Besides the demo, turn in a copy of the steps you have used to create it.

Make a demo to the instructor before or after a class or during the office hours. Progams must be able to be compiled and run in the machines of the lab.