### Home > CALC > Chapter 8 > Lesson 8.3.1 > Problem 8-101

The graph at right is

The

-axis.Vertical rectangles.

The

-axis.Horizontal rectangles would be very difficult (because the inverse of

is NOT a function). So use the Shell Method.The line

.By shells:

Where did the

come from?

Recall that each cylindrical shell is a prism with dimensions: (base)(height)(width).

Well,represents the (radius) in the circumference part of the formula:.

If we were rotating about the-axis (as in part (b)), then the radius would be the same as the bounds,.

But since we are rotating about a line that is parallel to the-axis, we do not want the radius to be the same as the bounds.

When we plug in the lower bound, we actually want a radius that is .

And when we plug in the upper bound, we actually want a radius that is .

will make this work! The line

.Vertical rectangles with a hole in the center.