For this project, you will design a beer glass by defining a function y = f(x) and rotating its graph about the x-axis to form a surface of revolution. Your design is subject to the following constraints:

• the glass must hold 1-1.5 pints;
• the base must have a diameter of 2-3 in;
• the top (opening) must have a diameter of 3-3.5 in;
• the height must be 5-7 in;
• the defining function y = f(x) must have a continuous, non-constant derivative throughout its domain; and
• the defining function cannot be a polynomial.

You can be very creative in defining your beer-glass functions, but be careful to satisfy the constraints.

1. Define a beer-glass function that satisfies the constraints listed above. Show that each constraint is satisfied.

2. Sketch a detailed graph of the function.

3. Write a paragraph that clearly describes your beer glass design. Write for a person with no knowledge of mathematics. Use correct grammar and spelling!
4. Sketch a detailed drawing of the beer glass you obtain by rotating the graph of your beer-glass function about the x-axis.
5. Set up the definite integral that gives the lateral surface area of your beer glass. Use your calculator or CAS to approximate the value of this integral.
6. Combine your results and ideas from problems 3 and 4 to make a ``poster'' advertising your design. It doesn't need to be a huge poster, an 8'' by 10'' poster will work just fine.