### Home > CALC > Chapter 8 > Lesson 8.1.5 > Problem 8-51

Using the methods you have learned, find the volume of the region bounded by: *y*=, *y*= 0, and*x*= 4,

revolved about the lines below. Use the steps outlined in problem 8-49. Homework Help ✎*x*-axis*y*-axis*x*= −2*y*= 5

After sketching an arbitrary rectangle (with Δ*x*→0), it is apparent that there will not NOT be a hole in the center of this solid.

That indicates that the Disk Method will be appropriate.

This arbitrary rectangle indicates that there will be a hole in the center of this solid. You will have to use the Washer Method.

Horizontal rectangles indicate that the bounds and the integrand will be in terms of *y*.

Notice that the figure will be a cylinder with a curvy hole in the center.

The radii of the cylinder is *R* = 4.

The radii of the curvy hole is *r* = *y*².

Q: Washers or disks? Think: Will there be a hole or won't there?

Q: Will the integral be in terms of *x* or *y*? Think: Are the rectangles vertical or horizontal?

Notice that these radii are 2 units longer than the radii in part (b). *R* = 2+4 *r* = 2 + *y*²

*R* = 5