The accompanying figure shows a spherical cap of heighth cut from a sphere of radius r

Chapter 6, Problem 26

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The accompanying figure shows a spherical cap of height \(h\) cut from a sphere of radius \(r\). Show that the surface area \(S\) of the cap is \(S=2 \pi r h\). [Hint: Revolve an appropriate portion of the circle \(x^{2}+y^{2}=r^{2}\) about the y-axis.]

Equation Transcription:

Text Transcription:

h

r

S

S=2 pi r h

x^2+y^2=r^2

Image text transcription: The accompanying figure shows a spherical cap of height h cut from a sphere of radius r. Show that the surface area S of the cap is S = 2πrh. [Hint: Revolve an appropriate portion of the circle x2 + y2 = r2 about the y-axis.]

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