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Tuesday, April 29, 2014

More Cube Problems, 2

Category: Solid Geometry

"Published in Newark, California, USA"

Plato (429 - 348 B.C.) was one of the first to discover a solution to that famous problem of antiquity, the duplication of a cube, i.e., the finding of the edge of a cube whose volume is double that of a given cube. 
One legend asserts that the Athenians, who were suffering from a plague of typhoid fever, consulted the oracle at Delos as to how to stop the plague. Apollo replied that the Delians would have to double the size of his altar, which was in the form of a cube. A new altar was constructed having its edge twice as long as that of the old one. But the pestilence became worse than before, whereupon the Delians appealed to Plato. Given that the side of the altar was 8 ft., find, accurate to five figures, the edge of the required altar.


To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Consider the first cube or old altar:

Consider the second cube or new altar:

Therefore, the edge of the required or new altar is