As they occur to me:

1) Remember that paraboloid? find a unit normal vector for the curved surface. (You may want to work in cylindrical coordinates.) Then, see if that leads to the correct value for the surface integral.

2) Calculate the moment of inertia for a cone of height h and base radius R.

3) An ant is following a spiral path along the outside of a cone of height 10 inches and base diameter 6 inches. This path winds twice around the cone, in a rational way, that is, when the ant is halfway up the cone, it has done one revolution around the cone's axis. If the ant is wearing a little ant pedometer, how many inches are counted off as the ant performs this trek?

4) The Amateur Foo-ball Players Association has decreed that a foo-ball's density shall increase as the square of the distance from the center of the ball. Moreover, each ball shall have a radius of 20 cm and a total mass of 800 g. Obviously the ball's density can be written as br^2, where b is some constant. Please determine that constant. Then, determine the moment of inertia of the foo-ball.

5) What charge density distribution produces an electric field of the form (0,Acos(by),0)?

6) Consider the surface z=ax^2 - by^2. Find an expression for the unit vector normal to this surface. Maybe you can calculate the area of the portion of this surface corresponding to x values between 0 and L and y values between 0 and h.

7) Consider the function f(x, y, z) = (x/3m +y/2m - z/5m)50 kg. By how much does f change if you step 40 cm in the northwest direction? (Assume east is in the positive x-direction and north is in the positive y-direction.)