### Home > APCALC > Chapter 9 > Lesson 9.3.1 > Problem 9-80

9-80.

Write the integral that calculates the volume generated when the region bounded by and

*is rotated:*

Sketch the region and determine the points of intersection.

About the

-axis.The outside radius (

) is the curveThe inside radius (. ) is the curve. This will be a "" integral, so make sure your radii expressions are in terms of.About the

-axis.Identify which curve will be the outside radius and which curve will be the inside radius. This will be a "

" integral, so make sure your radii expressions are in terms of.About the line

.Since

is a vertical line, this will be similar to part (b). This time the outside radius will beand the inside radius will be .