You are given a sphere of radius R units. Units may be any units of length: inches, cm, metres, feet, miles, km.
A Sphere is a 3D locus of points which are all equidistant from the centre of the sphere. (4/3) * π * Radius^{3} 4 * π * Radius^{2 }
Great Circles and Small Circles
A great circle is a circular ring on the sphere, the centre for which, coincides with the centre of the sphere. So the radius of the Great Circle is same as that for the sphere.
A small circle of a sphere, is a circle drawn on the sphere, with lesser radius than the sphere itself.
An example of a Zone of a Sphere or Frustum of a Sphere Total surface area of a zone or frustum = 2 π R h + π r_{1}^{2}π r_{2}^{2} Volume of a zone or frustum = (3r_{1}^{2} 3r_{2}^{2 }^{2} π h/6 Cubic Units
Volume =_{1}^{2} 3r_{2}^{2 }^{2} π h/6 Cubic Units
Curved surface area of the zone = 2 π R h Square Units Area of the upper base = π r_{1}^{2}Square Units Area of the lower base = π r_{2}^{2 }Square Units Total Surface Area = (2 π R h + π r_{1}^{2} π r_{2}^{2}^{ }Square Units _{}
Mensuration for a Spherical Cap
What is the volume of a spherical cap of height h units?
As derived here(3R  h) πh^{2}
Height of the geometric centroid above the centre of the sphere = (3 (2R  h) ^{2}4 (3R  h) units
Mensuration for a Hemisphere Let's cut the sphere into two hemispheres. What is the volume and total surface area, for either of the hemispheres? Volume of the hemisphere = (2/3) * π * Radius^{3 } Surface Area of the hemisphere = Curved surface area + area of base = 2 * π * Radius^{2 }π * Radius^{2 }= 3 π Radius^{2 } ^{} ^{} ^{} What is the volume of material used in a sphere of radius 11.0 units a hollow sphere of thickness 2 units?
Inner radius = Outer Radius  Thickness. So the volume of the spherical gap inside = (4/3)π*(Inner Radius)^{3 } Geometric Properties of a sphere which is of radius 12: Properties like Surface Area, Volume and other aspects of mensuration. Geometric Properties of a sphere which is of radius 13: Properties like Surface Area, Volume and other aspects of mensuration. properties of a Sphere tutorial over hereCommon CoreGCSE
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