What you're being asked is to evaluate a solid of revolution.

You need to imagine the region under the graph as a series of rectangles. These rectangles get rotated to form cylinders.

The cylinders have a radius the same as the value of the graph at that point, so the radius of each cylinder is . Therefore the area of each circular cross-section is .

We will call the height of each cylinder , which is a small change in .

So the volume each cylinder is and the volume of the solid can be approximated by .

As you increase the number of cylinders and make the height of each cylinder , this sum converges on a definite integral, and the approximation becomes exact.

So .

You should find that this integral converges...