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Mensuration 99e Archimedes Sphere and Cylinder

Shape and Space PowerPoint Presentation

Mensuration 99e Archimedes Sphere and Cylinder

In determining the formulae for the surface area and volume of a sphere, Archimedes discovered the extraordinary fact that if you envelop the sphere perfectly with a cylinder, the cylinder will have both a volume and a surface area that are exactly 1 1/2 times those of the sphere. He was so overjoyed at discovering this remarkable relationship between these shapes that he had them inscribed on his tombstone together with the ratio 3:2.
This is what the presentation is about and it gives the students the opportunity to derive both relationships for themselves. A couple of nice problem on spheres in a cylinders follow.

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