Okay, so the idea is that your shape will resemble a cone or in many of these cases the outside surface of the cone. The tangent from Q20a is

.
Now the concept of integrating is to find the section under the curve.
Combining Q20a and what we know you are integrating

. Now when you are finding the volume of several boundaries you are simply finding the volume of a cone.
When you are rotating around the x-axis you are treating the height of x as Infinitismal height which then becomes dx and then the radius of the cone is y so you are working with

. To finish this off sub the equation for y and use reverse chain rule. Note the boundaries represent the height of the structure.
Similarly rotation around the y-axis implies that you treat the y-axis as height and the x-axis as radius.
For part b there is a clever way of doing the question. Find the volume of the solid formed when the region is rotated around the y-axis for just

take away the volume from

.
For part b you are working with
^{\frac{2}{3}}dy+\int_{0}^{3}\frac{y^{2}}{9}dy\right))