Get answer: 5559 These exercises reference the Theorem of Pappus:If R is a bounded plane

Chapter 14, Problem 59

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55–59 These exercises reference the Theorem of Pappus: If \(R\) is a bounded plane region and \(L \)is a line that lies in the plane of \(R\) such that \(R\) is entirely on one side of \(L\), then the volume of the solid formed by revolving \(R\) about \(L\) is given by

volume = (area of \(R\)) · (distance traveled by the centroid)

Use the Theorem of Pappus to find the centroid of the triangular region with vertices

 \((0,0),(a, 0), \text { and }(0, b), \text { where } a>0 \text { and } b>0 \text {. }\)

 \(\text { [Hint: Revolve the region about the } x \text {-axis to obtain } \bar{y} \text { and about the } y \text {-axis to obtain } x \text {.] }\)

Equation  Transcription:

Text Transcription:

(0,0),(a,0),(0,b)

a>0

b>0

X-axis

Y bar

Y-axis

X bar