To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
No jsMath TeX fonts found -- using image fonts instead.
These may be slow and might not print well.
Use the jsMath control panel to get additional information.
jsMath Control PanelHide this Message

jsMath
Loading jsMath...

Den Hartog’s Mechanics

A web-based solutions manual for statics and dynamics

Problem 66

OK, we learned in Problem 64 that the centroid of a semicircular arc is 2 r/ \pi from its center. If we spin that semicircular arc around to make a sphere, the centroid will make a circle with arc length 2\pi (2r/\pi) = 4r. The arc length of the generating semicircle itself is \pi r, so Pappus’s first theorem would tell us that the surface area of the generated sphere is

(\pi r)(4r) = 4 \pi r^2

which is, in fact, what any handbook (or nice web site) would tell you.

Problem 67Problem 65

Last modified: January 22, 2009 at 8:32 PM.