# 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 whenever a surface wants to be as small as possible. Examples include bubbles and water drops. Can you think of more?

## The Earth

The Planet Earth, our home, is nearly a sphere, except that it is squashed a little at the poles.

It is a spheroid, which means it just misses out on being a sphere because it isn't perfect in one direction (in the Earth's case: North-South)

## Volume and Surface Area

Surface Area = 4 × π × r2

### Example: r = 5

 Surface Area = 4 × π × r2 = 4 × π × 52 = 4 × π × 25 = 100 π ≈ 314

Volume = (4/3) × π × r3

### Example: r = 5

 Volume = (4/3) × π × r3 = (4/3) × π × 53 = (4/3) × π × 125 = (500/3) × π ≈ 524