Ball (mathematics) facts for kids

In Euclidean space, a ball is the volume bounded by a sphere

In mathematics, a ball is like the inside of a sphere. Think of a basketball: the surface is the sphere, and everything inside it is the ball. It's also sometimes called a solid sphere.

A ball can be "closed," meaning it includes its outer surface (the sphere). Or it can be "open," meaning it includes everything inside but not the surface itself.

These ideas aren't just for 3D shapes. They work for shapes in different dimensions too! For example, in a 2D flat space (like a piece of paper), a "ball" is actually a disk (a flat circle, including its inside). In a 1D space (like a line), a "ball" is just a line segment.

Sometimes, people use the word "sphere" when they really mean "ball," especially in everyday talk. But in math, they are different!

Balls in Different Dimensions

In math, we can talk about balls in different dimensions. This helps us understand shapes in a more general way.

What is a Ball in 1D, 2D, and 3D?

• 1-ball: Imagine a line. A 1-ball is a line segment. It's like a small piece of that line.
• 2-ball: In a flat, 2D space (like a tabletop), a 2-ball is a disk. This is a circle and everything inside it. It's bounded by a circle.
• 3-ball: In our everyday 3D world, a 3-ball is what we usually think of as a ball. It's the space inside a sphere. It's bounded by a 2-dimensional sphere.

So, a ball is always the "filled-in" part of a shape, while a sphere is just the outer surface.

How Big is a Ball? (Volume)

Every ball has a size, which we call its volume. The volume tells us how much space the ball takes up. For a ball in 3D, we can measure its volume in cubic units (like cubic centimeters or cubic inches).

The volume of a ball depends on its radius (the distance from its center to its surface) and the number of dimensions it's in. The bigger the radius, the larger the volume of the ball.

Parts of a Ball (Regions)

You can cut a ball into different parts, and each part has a special name:

• Spherical cap: This is like the top part of a ball, cut off by a flat plane. Think of slicing off the top of an orange.
• Spherical sector: This is a cone-shaped part of a ball. Imagine a slice of pie, but in 3D, with the pointy end at the center of the ball.
• Spherical segment: This is a part of a ball cut by two parallel flat planes. It's like a thick slice from the middle of an orange.
• Spherical shell: This is the space between two balls that share the same center but have different sizes. Think of a hollow ball, like a tennis ball, where the shell is the rubber part.
• Spherical wedge: This is like a slice of an orange that goes all the way to the center. It's bounded by two flat planes that meet at the center of the ball.

See also

In Spanish: Bola (matemática) para niños