Spheres Overview
Sphere Facts
Notice these interesting things:
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
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 × 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
≈ 524
Hemisphere
A hemisphere is an exact half of a sphere.
Other Cool Spheres
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)
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
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?
| 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) |
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
≈ 524
Hemisphere
A hemisphere is an exact half of a sphere.
Other Cool Spheres
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