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

Chapter 14, Problem 57

(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 fact that the area of an ellipse with semiaxes \(a \text { and } b \text { is } \pi a b\)to find the volume of the elliptical torus generated by revolving the ellipse

\(\frac{(x-k)^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)

about the \(y \text {-axis. Assume that } k>a \text {. }\)

Equation  Transcription:

text transcription:

Pi ab

(x-k)^2/a^2 + y^2/b^2 = 1

Y-axis

k>a