Sane or not, it is correct, but more surprising perhaps, would be that if Ma Bell did the same thing to the circumference of every planet in the solar system (add 50 ft to the circumferenc) the height of every one of the cables thus hung would be exactly the same height from the surface of the planet. Insane... yes, Insanely beautiful that reality defies our perceptions, but not our mathematical logic.
How can adding 50' of slack to the cable spread evenly around the equator add 8' at each point? Your math was impeccable but your answer does not pass the sanity check! This is why we must not blindly accept mathematical results. That is the lesson to be learned from this geometry problem.
firstname.lastname@example.org wrote in article <Pine.PMDF.3.91.961104130200.557939369Aemail@example.com>... > > > On Mon, 4 Nov 1996, mfr1 wrote: > > > Ma Bell wants to place a telephone cable around the equator. She adds 50 > > feet to the length of the cable beyond what is required. This slack in the > > cable allows the cable to be strung up above the ground. How high up from > > the surface of the earth will the cable stand? You can assume that the > > earth is a perfect sphere. > > > > In your mind, run a sanity check on your answer to see if it makes sense. > > > Surprisingly, you will be able to walk under the cble easilty. Since the
> circumference of a circle is C = 2piR, each increase in R obf 1 foot > increases the circumference by 2pi feet. since the cable has been > increased by 50 feet the radius of the cable-circle will be increased by > 50/2pi or about 8 feet! > > Alan Lipp >