Frank and the LP
FRANK the Engineer was an avid music fan. He used to save all the money that he could find down the back of the sofas at his relatives' homes until he had enough to buy another gramophone record containing his favourite classical music. Frank loved rushing home to slip on his headphones and sink into the other world that classical music can produce for some. He had to wear headphones because his wife was fanatical about Guns & Roses and absolutely hated Frank's taste in music.
His latest purchase was Ravel's "Bolero", for he had just seen the movie of the same name starring Bo Derek and expected to get the same experience from the music as he did from the pictures. Just before he put the needle of the record player onto the spinning disk, a thought came over him. He quickly took the record off the turntable and did some measurements.
He noted that the record was 30 cm in diameter. The groove started one centimetre from the outside edge, and the internal circle where the groove ended had a diameter of 10 cm. Then, taking out a magnifying glass, he counted up that there were exactly 24 grooves per centimetre (of course, there's only one groove, but you know what I mean), and that this was uniform across the whole playing surface.
Then he went to the drawing board and started calculating - and he's still at it. Can you work it out? With all of the information given above, how far will the needle travel if the record side is played from start to finish? Please supply your answer in metres and to the nearest centimetre only.
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