text: # 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.
explanation: The document provides a detailed explanation of the properties of a sphere, including its definition, real-life examples, and mathematical properties such as radius, diameter, and great circles. It also includes formulas for the volume and surface area of a sphere. The document does not contain any specific questions or answers.
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distilabel_metadata.content: # 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation of the properties of a sphere, including its definition, real-life examples, and mathematical properties such as radius, diameter, and great circles. It also includes formulas for the volume and surface area of a sphere. The document does not contain any specific questions or answers.
  
  Label: no-question