# Sphere

A sphere is a 3D geometric figure that has a round shape. All points on the surface of the sphere are an equal distance from its center.

Below are some real-life examples of spheres. A basketball, the Earth, and an orange are all examples of geometric figures that have the shape of a sphere.

## Properties of a sphere

In Geometry, a sphere is defined as the set of all points in space that are equidistant from a fixed point (the center) of the sphere.

A radius, r, of a sphere is a line segment from the center of the sphere to any point on the sphere's surface. Three radii (plural for radius) are graphed for the sphere with center at point O below.

### Diameter

Like a circle, a diameter of a sphere is any chord that passes through its center, as shown below.

### Great circle

The intersection of a plane and a sphere containing the sphere's center creates a circle. This circle is called a great circle. A plane that intersects a sphere without going through the center will also create a circle. However, it is not a great circle, since a great circle is the largest possible circle that can be created by the intersection of a plane with a sphere. Any other circular intersection has a radius smaller than the great circle.

Plane P above intersects sphere O through center O creating a great circle of the sphere, shown in grey. The great circle divides the sphere into two equal hemispheres.

Three great circles in black, red, and green are shown for sphere O above. A sphere contains infinitely many great circles. Each great circle is considered a plane of symmetry since it divides the sphere into two equal parts. This means that a sphere has infinitely many planes of symmetry.

## Volume of a sphere

The volume, V, of a sphere is

where r is the radius of the sphere.

## Surface area of a sphere

The surface area, S, of a sphere is

S = 4πr2

where r is the radius of the sphere.
The text passage provides a detailed explanation of the properties of a sphere, including its definition, real-life examples, and mathematical formulas for volume and surface area. It does not contain any specific mathematical questions or answers.
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Given a text passage, determine:
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    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

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TYPE: <one of the following values>
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system
# Sphere

A sphere is a 3D geometric figure that has a round shape. All points on the surface of the sphere are an equal distance from its center.

Below are some real-life examples of spheres. A basketball, the Earth, and an orange are all examples of geometric figures that have the shape of a sphere.

## Properties of a sphere

In Geometry, a sphere is defined as the set of all points in space that are equidistant from a fixed point (the center) of the sphere.

A radius, r, of a sphere is a line segment from the center of the sphere to any point on the sphere's surface. Three radii (plural for radius) are graphed for the sphere with center at point O below.

### Diameter

Like a circle, a diameter of a sphere is any chord that passes through its center, as shown below.

### Great circle

The intersection of a plane and a sphere containing the sphere's center creates a circle. This circle is called a great circle. A plane that intersects a sphere without going through the center will also create a circle. However, it is not a great circle, since a great circle is the largest possible circle that can be created by the intersection of a plane with a sphere. Any other circular intersection has a radius smaller than the great circle.

Plane P above intersects sphere O through center O creating a great circle of the sphere, shown in grey. The great circle divides the sphere into two equal hemispheres.

Three great circles in black, red, and green are shown for sphere O above. A sphere contains infinitely many great circles. Each great circle is considered a plane of symmetry since it divides the sphere into two equal parts. This means that a sphere has infinitely many planes of symmetry.

## Volume of a sphere

The volume, V, of a sphere is

where r is the radius of the sphere.

## Surface area of a sphere

The surface area, S, of a sphere is

S = 4πr2

where r is the radius of the sphere.
user
The text passage provides a detailed explanation of the properties of a sphere, including its definition, real-life examples, and mathematical formulas for volume and surface area. It does not contain any specific mathematical questions or answers.

TYPE: NO_QUESTION