   Chapter 5.2, Problem 21E

Chapter
Section
Textbook Problem

# Refer to the figure and find the volume generated by rotating the given region about the specified line. ℛ 1 about AB

To determine

To find:

The volume generated by rotating the region R1 about the line  AB by using the figure.

Explanation

1) Concept:

i. If the cross section is a disc and the radius of the disc is in terms of x  or y then the area is A=π radius2

ii. The volume of the solid revolution about the y-axis is

V= abA(y)dy

2) Given:

Figure:

3) Calculation:

Here, OB appears to be the line y=x and AB appears to be the line x=1.

Rotating R1 about AB that is the line  x=1, the cross section is perpendicular to the y-axis and it is a disc with the radius r=1-y because it is the distance from the line OB (y=x)  to the axis of the rotation line AB (x=1).

From the figure, the solid lies between y=0 and  y=1

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