We are finding the volume using the technique of slices.

Recall that , where is the area of each slice.

To find out the area of each slice, we need to know the length of one side.

Since the region is an ellipse:

we can figure out that the distance between each side of the ellipse could be defined as

Thus, the area of each square slice will be

Thus, the volume of the solid would be .

Does this make sense? If you have a question, feel free to ask.

--Chris