# Sphere

*Go to Surface Area or Volume.*

Sphere Facts

**Notice these interesting things:**

- It is perfectly symmetrical
- All points on the surface are the

same distance**"r"**from the center - It has
**no**edges or

vertices (corners) - It has one
**surface**

(not a "face" as it isn't flat) - It is
**not**a polyhedron

*Glass Sphere*.

Balls and marbles are shaped like spheres.

## Largest Volume for Smallest Surface

Of all the shapes, a sphere has the smallest surface area for a volume. Or put another way it can contain the greatest volume for a fixed surface area.

Example: if you blow up a balloon it naturally forms a sphere because it is trying to hold as much air as possible with as small a surface as possible. Press the Play button to see.

## In Nature

The sphere appears in nature when a surface wants to be as small as possible. Examples include bubbles and water drops. Can you think of more?

## Volume and Surface Area

Surface Area = 4 × π × r^{2}

### Example: r = 5

^{2}

^{2}

Volume = (4/3) × π × r^{3}

### Example: r = 5

^{3}

^{3}

Try dragging point "A":

Also see Volume and Area of a Sphere Calculator

## Spheroid

## The EarthThe Planet Earth, our home, is | So it is technically a spheroid, but a very mild version of one. | |

Here is a more extreme spheroid: |

## Hemisphere

A **hemisphere** is an exact half of a sphere.

## Other Cool Spheres