I'll get you started with the first problem. The method is called Disk Method and we use it whenever the region that's being revolved is adjacent to the rotational axis.

The formula is INTEGRAL Pi (RADIUS^2) dx from x=a to x=b.

The RADIUS is the distance from the curve to the rotational axis, in your case it is simply the y-coordinate, so R(x) = -x^3 + 4x

Set up the integral from x=0 to x=2.

Good luck!