Sphere

Go to Surface Area or Volume.

Sphere Facts

Notice these interesting things:

Sphere Radius

  • It is perfectly symmetrical
  • All points on the surface are the
    same distance from the center
  • It has no edges or
    vertices (corners)
  • It is not a polyhedron
Glass Sphere
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.

Earth is a Spheroid
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

Sphere Radius

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

Other Cool Spheres

Jade Sphere Light Sphere
Dark Sphere Brass Sphere