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Archimedes (Tombstone with Sphere and Cylinder)

Enrichment PowerPoint Presentation

Archimedes (Tombstone with 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 problems on spheres in cylinders follow. There are printable worksheets for students should you wish to use them.
This is a nice piece of enrichment material and the exposure of the content (through this medium or any another) to appropriate top sets should be considered essential if we are to motivate them to study higher mathematics.

This is the same presentation as Mensuration 99e in Shape and Space and appears naturally there after students have UNDERSTOOD how the volume of a sphere is determined and can use the formula.

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