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Surface area of spheres (demonstration)

Surface area of spheres (demonstration)

The surface of a sphere consists of the set of points which are all at the same distance from a given point in space.

Mathematics

Keywords

surface of sphere, great circle, mathematics, geometry, surface

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Scenes

Sphere

A sphere is defined by the set of points which are all at a fixed distance (r ) from a given point in space (P ). Here r is the radius of the sphere.

If this distance is smaller than r it results in a spherical body, if it is exactly equal to r it results in a spherical surface.

The intersection of a sphere with a plane, which passes through the centre of the sphere, is called the great circle of the sphere. This is demonstrated by pressing the ´Animation´ button.

Great circles and the sphere

  • great circle

The area of a great circle is

and the area of the four great circles together is

which is the formula of the surface area of the sphere.

In other words, 4 great circles can cover the entire surface of the sphere. Of course, this does not work in reality, this is only a theoretical experiment.

Animation

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