Sphere got originated from a Greek name sphaira which means globe or ball. A sphere is a three dimensional figure which is perfectly round in shape. It is just like a circle which is a set of points which are of same distance that is called radius from the centre of it.
A sphere is perfectly symmetrical and it has no edges or vertices. There are many real life examples of sphere. There are many objects which we use in our day to day life that are in shape of sphere. Objects like football, volleyball, throw ball, etc., are said to have shape of a sphere. In solid geometry, the generated by revolving a circular lamina about any of its diameters, is called a sphere.
The centre and radius of this circle are called respectively the centre and the radius of the sphere. All the points on the surface are equidistant from the centre.
Formula for sphere:
For a solid sphere of radius ‘r’ units, we have:
• Volume of the sphere – Volume of the sphere is the capacity of it. The volume of sphere is:
4/3 . pi . r^3 cubic units.
• Surface area of the sphere – The surface area of sphere is:
4. pi. r^2
For example: Consider a sphere of radius 3 cm then the volume of sphere will be: 4 .pi (3)^3 = 339.12 cubic cm and its surface are will be 113.04 sq. cm
Spherical shell - The solid enclosed between two concentric spheres is called a spherical shell. For a spherical shell with external radius R and internal radius r we have:
• Volume of the spherical shell is:
4/3 pi (R^3-r^3) cubic units
Hemisphere - When a plane through the centre of a sphere cuts it into two equal parts, then each part is called a hemisphere.
For a hemisphere of radius r, we have:
• Volume of the hemisphere is half of the volume of sphere which is 2/3. Pi . r^3 cubic units.
• Curved surface area of the hemisphere is half of the surface area of sphere which is 2. Pi . r^2 square units
• Total surface area of the hemisphere is 3pi. r^2 square units.
Equation of sphere
The equation of sphere with radius ‘r’ and center (a, b, c) is: (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2
For a sphere of radius ‘r’ centered at origin is x^2 + y^2 +z^2 = r^2
This is the sphere equation.
A sphere is perfectly symmetrical and it has no edges or vertices. There are many real life examples of sphere. There are many objects which we use in our day to day life that are in shape of sphere. Objects like football, volleyball, throw ball, etc., are said to have shape of a sphere. In solid geometry, the generated by revolving a circular lamina about any of its diameters, is called a sphere.
The centre and radius of this circle are called respectively the centre and the radius of the sphere. All the points on the surface are equidistant from the centre.
Formula for sphere:
For a solid sphere of radius ‘r’ units, we have:
• Volume of the sphere – Volume of the sphere is the capacity of it. The volume of sphere is:
4/3 . pi . r^3 cubic units.
• Surface area of the sphere – The surface area of sphere is:
4. pi. r^2
For example: Consider a sphere of radius 3 cm then the volume of sphere will be: 4 .pi (3)^3 = 339.12 cubic cm and its surface are will be 113.04 sq. cm
Spherical shell - The solid enclosed between two concentric spheres is called a spherical shell. For a spherical shell with external radius R and internal radius r we have:
• Volume of the spherical shell is:
4/3 pi (R^3-r^3) cubic units
Hemisphere - When a plane through the centre of a sphere cuts it into two equal parts, then each part is called a hemisphere.
For a hemisphere of radius r, we have:
• Volume of the hemisphere is half of the volume of sphere which is 2/3. Pi . r^3 cubic units.
• Curved surface area of the hemisphere is half of the surface area of sphere which is 2. Pi . r^2 square units
• Total surface area of the hemisphere is 3pi. r^2 square units.
Equation of sphere
The equation of sphere with radius ‘r’ and center (a, b, c) is: (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2
For a sphere of radius ‘r’ centered at origin is x^2 + y^2 +z^2 = r^2
This is the sphere equation.
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