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The riddle of the moon 2

The riddle of the moon 2

There is an irresistible fascination with everything that has to do with the moon. Two centuries ago someone launched the great Moon Bulo, which spread like wildfire because people are willing to believe anything. It was based on the supposed wonderful powers of a telescope that, it was said, let us see the tiniest objects on the lunar surface. Imagine, people turned on that supposed telescope with such credulity, that those who invented the bulo published very detailed illustrated descriptions of the inhabitants of the moon and its surroundings so well done that despite the extravagance of history, it He believed them for decades.

Conjectures regarding the state of lunar affairs have always been in fashion among theorists and writers since time immemorial.

Four centuries ago, Ariosto, in his "Orlando Furioso" sent Astolfo on a random and rugged journey, in which he discovered a narrow valley where the office of lost objects of the earth was, which were none other than unsatisfied, lost human desires . Cyrano de Bergerac's trip to the Moon is one of the funniest contributions to lunar literature and Julio Verne's account of an air trip is the most exciting of all legends. However, the shortest trip known is that of Edgar Allan Poe's hero Hans Pfeel, of Rotterdam, who completed the trip in 19 hours by means of a balloon.

And this was the story that stimulated the imagination of a well-known professor named Spearwood, who organized a similar balloon trip, convinced that at a certain distance from the earth he would pierce the power of attraction of the earth and enter that of the moon.

I explain this to you because our problem has to do with your adventure before it was released from its earthly connections.

The globe was connected by a steel cable to a ball 24 inches in diameter, the steel being 1/100 inch thick. It seems hard to calculate the length of a 1/100 inch cable wound on a 24-inch diameter ball, but in reality it is so simple that if we limit ourselves to common sense, it will not be necessary to deepen much. In fact I encourage you to try to solve this problem without using just math, so that even a child could understand it.

Solution

To solve this problem without using pi, it is necessary to remember the great discovery of Archimedes that the volume of a sphere is equal to two thirds of the volume of a cylindrical box in which the sphere exactly fits. The cable sphere has a diameter of 24 inches, so that its volume is equal to that of a cylinder 16 inches high and with a base diameter of 24 inches.

Now, the cable is simply an extended cylinder. How many parts of cable, each 16 inches high and one hundredth of an inch in diameter, are equal in volume to the 16-inch-high and 24-inch base diameter cylinder? The surfaces of the circles keep each other the same proportion as the squares of their diameters. The square of 1/100 is 1 / 10,000, and the square of 24 is 576, so we conclude that the volume of the cylinder is equal to 5,760,000 of the 16-inch long cables. The total cable length, therefore, is 5,760,000 by 16, or 92,160,000 inches.