Many know the learned Archimedes, especially for the levers. Volume calculation the area was one of the more believed that Archimedes discoveries of all he did in his life. He came to demonstrate in a very original way that the volume of the sphere is equal to two thirds of the volume of circular cylinder confined to it. He was so impressed that he himself (perhaps because at that time there was talk of perfect bodies) who commanded in his grave this figure is recorded in memory of the best of their ideas.
Archimedes figured a hemisphere and next to it a right circular cylinder and right cone, both as a base circle of the hemisphere.
obtained in the cylinder is a circle of radius R (note that the radius is half the diameter d). In the area also will be a circle, but his radio depends on the distance d. Looking at the figure below, remembering the Pythagorean theorem, you can easily write that if the radius of the section is r, then d2 = r2 + R2.
cylinder = Volume Volume Volume + cone hemisphere
But, like Archimedes well knew,
Volume cylinder = PR3;
Cone Volume = PR3 / 3 and so was
hemisphere volume = 2PR3 / 3 Volume sphere = 4PR3 / 3.
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