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 SurfaceOf 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 EarthThe 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 × r^{2}
Example: r = 5
Surface Area | = 4 × π × r^{2} | |
= 4 × π × 5^{2} | ||
= 4 × π × 25 | ||
= 100 π | ||
≈ 314 |
Volume = (4/3) × π × r^{3}
Example: r = 5
Volume | = (4/3) × π × r^{3} | |
= (4/3) × π × 5^{3} | ||
= (4/3) × π × 125 | ||
= (500/3) × π | ||
≈ 524 |
Other Cool Spheres