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

Chapter 14, Problem 56

(choose chapter or problem)

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 and the result of Example 3 to find the volume of the solid generated when the region bounded by the \(x-a x i s\) and the semicircle \(y-\sqrt{a^{2}-x^{2}}\) is revolved about

\(\text { (a) the line } y=-a\)                 \(\text { (b) the line } \mathrm{y}=\mathrm{x}-\mathrm{a} \text {. }\)

Equation  Transcription:

text transcription:

Y-square root a^2-x^2

X-axis

y=-a

y=x-a