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On the sphere and cylinder

On the Sphere and Cylinder

Archimedes is famous for huge discoveries. His works mostly concentrated on exploring the fundamental principles of mechanics, hydrostatics and the properties of geometric entities like circles, spheres, spirals and cylinders. But, discovery that claimed him as best mathematician was, when he find the relationship between a sphere and circumscribing cylinder of the same height and diameter. He wrote 'On the Sphere and Cylinder' in two volumes and published it in 225 BC.

There was not much known about the value of the ratio between the circumference and diameter of a circle, and it was impossible to evaluate ratios using irrational numbers with the number system at that time. But still Archimedes showed that the volume and surface area of the sphere are two - third's of its circumscribing cylinder including the surface on its top and bottom.

He found the Volume of sphere as 4/3 πr3 , and that of cylinder of the same height and Diameter as 2 πr3. The Surface area was 4 πr2 for the sphere, and 6 πr2 for the cylinder including the two bases.

He proved three major results. First thing he stated was 'The volume of a sphere is equal to 4 times the area of the largest circle it contains'. Second was 'The curved surface are of a spherical cap is equal to the area of a circle with radius equal to the distance between the vertex at the curved surface and the base of the spherical cap'. Here he proves spherical cap is greater than and less than the semi - circle respectively. Finally he stated was 'The cylinder with the large circle of a sphere as base and diameter as height has a volume times of the sphere'.

Archimedes was so pleased with his discovery on Sphere and Cylinder, So he requested his kinsman and friends that he should be buried over the Graveyard with the sculpted sphere and cylinder, placed on his tomb.

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Daily Maths Topic Today - on the sphere and cylinder.

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