Volume with Parametric Equations

I've been banging my head against this for a couple days now. The first question is to find the area and the second question (where I am really getting stuck) is to take that area and find a volume. This question is from school but I only have one example in my notes and as much as I look at it...it still makes no sense to me.

The Parametric Equations are as follows:

and

Question 1: Find the area between the curve and the y-axis from to

So I set this up as Area =

When

Area = and I worked this out to be Area =

Question 2: What is the volume if the area (in question 1) is revolved about the x-axis?

This is where I am stuck. The first question may be wrong but atleast I can begin to work it. I don't know where to start setting up the integral to find the volume. I am thinking that the set up will have two integrals: One for the two horizontal lines that go from points and to the y-axis; and one for the parametric curve.

I have been trying to use the shell method with the shell radius being , and but I don't feel comfortable with anything I have set up.

I would greatly appreciate any help you can offer.

Thank you in advance.