 Hi, everyone. This example problem will walk you through how to find the volume of a solid of revolution by using the disk method. So in this problem we are asked to find the volume of a solid formed by revolving the region bounded by f of x equals 2 minus x squared and g of x equal to 1 about the line y equals 1. So if you go ahead and graph those on your calculator I've done the same here and you should obtain a graph that looks like this. I did alter my window a little bit so you can do the same if you wish. You can see in blue the upside down parabola that is the function f of x equals 2 minus x squared and the red line is the line y equals 1. That also is our axis of revolution. So we're trying to revolve around that line y equals 1 the region in between the two curves that you see here in yellow. So if you imagine taking that yellow region and revolving it around that horizontal line it's going to come down to here and it forms what looks to be almost like a football shape. So according to the disk method the representative rectangle that we draw is going to have two characteristics. It's going to be perpendicular to your axis of revolution and also touching it. So as we saw in the lesson imagine having infinitely many rectangles and we're simply choosing one to use as our demonstration. So we would be taking that representative rectangle and revolving it flipping it around that axis of revolution. Therefore it forms a disk. So the way in which we get a volume by using this disk method one part that we need is the length of our representative rectangle that we'll call capital R and the way in which we can get the length of that rectangle is thinking of it as top minus bottom and since it's a dx problem our expression does have to be in terms of x. So let's go ahead and set that up. So at the top the rectangle is hitting the parabola at the bottom it's hitting that line y equals 1. So we can simplify that to get 1 minus x squared. So to get the volume then our limits of integration need to be x's so if we take a look at our graph you would have to find these points of intersection right here and here you're welcome to do that on your graphing calculator you will find that they intersect at negative 1 and positive 1 so those become our limits of integration. The rule goes that we're doing pi times that r value squared. You are welcome to evaluate that on your calculator either with or without including pi right away. If you want an answer in terms of pi and just do the definite integral itself you should get 1.06 repeating and then that of course would have to be multiplied by pi. If you want a pure decimal answer and multiply the pi in you should get approximately 3.351. If you did need units attached to your answer remember this is a volume problem therefore your units would be in cubic units.