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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.