In Exercises 57 and 58, use the Second Theorem of Pappus, which is stated as follows. If
Chapter 7, Problem 57(choose chapter or problem)
In Exercises 57 and 58, use the Second Theorem of Pappus, which is stated as follows. If a segment of a plane curve C is revolved about an axis that does not intersect the curve (except possibly at its endpoints), the area S of the resulting surface of revolution is given by the product of the length of C times the distance d traveled by the centroid of C.
A sphere is formed by revolving the graph of \(y=\sqrt{r^{2}-x^{2}}\) about the axis. Use the formula for surface area, S = 4𝜋r2, to find the centroid of the semicircle \(y=\sqrt{r^{2}-x^{2}}\).
Equation Transcription:
Text Transcription:
y=sqrtr^2 -x^2
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