A sphere is formed by revolving the graph of about the axis. Use the formula for surface
Chapter 7, Problem 55(choose chapter or problem)
Second Theorem of Pappus In Exercises 55 and 56, 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 equal to 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 x-axis. Use the formula for surface area, \(S=4 \pi r^{2}\), to find the centroid of the semicircle \(y=\sqrt{r^{2}-x^{2}}\).
Text Transcription:
y=sqrt r^2-x^2
S=4 pi r^2
y=sqrt r^2-x^2
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