# Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x -axis.

### International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
ISBN: 9781305501607

### International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
ISBN: 9781305501607
Chapter 8, Problem 8.43P
Textbook Problem
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## Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.

To determine

Centroidal coordinates of the volume obtained by revolving the area about x-axis.

### Explanation of Solution

Given Information:

The following plane in given,

Calculation:

Consider the following figure,

Consider the revolution of a rectangular strip about x-axis as shown in figure above.

The volume generated by the strip is, dV=πy2dx=π(h( 1 x 2 / b 2 ))2dx

Integrate the differential volume to get the total volume as,

V=dV=π0b ( h( 1 x 2 / b 2 ) )2dxV=πh20b[1+ x 4 b 4 2 x 2 b 2 ]dxV=πh2[x+x55b42x33b2]0b

V=πh2[b+ b 55 b 42 b 33 b 2]V=πh2[b+b52b3]V=8πbh215

By symmetry the y-coordinates of centroid is y¯=0

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