**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

**Related items**

### 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 (

**). Here**

*P***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

### Related items

#### Sphere

A sphere is the set of points which are all within the same distance from a given point in space.

#### Four colour theorem

Colour a map with the fewest number of colours possible, so that no two adjacent regions have the same colour.

#### Non-orientable surfaces

The Möbius strip and the Klein bottle are special two-dimensional surfaces with only one side.

#### Perimeter, area, surface area and volume

This animation presents the formulas to calculate the perimeter and area of shapes as well as the surface area and volume of solids.

#### Volume of spheres (Cavalieri´s principle)

Calculating the volume of a sphere is possible using an appropriate cylinder and cone.

#### Volume of spheres (demonstration)

The sum of the volume of the ´tetrahedrons´ gives an approximation of the volume of the sphere.

#### Geometric transformations – rotation

This animation demonstrates geometric rotation, a type of geometric transformation both in plane and space.

#### Solids of revolution

Rotating a geometric shape around a line within its geometric plane as an axis results in a solid of revolution.