Volume of a Sphere

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What is a Sphere?

A three-dimensional geometric shape, the sphere is completely round, like a ball. A sphere has a set of all points in space positioned at a fixed distance (known as a radius) from a single point that is the center of the sphere.

The following are the properties of a sphere:

  • A sphere is a three-dimensional object with three dimensions: length, width, and height (or radius).
  • Completely round in shape, and therefore, it has no edges or vertices (corners).
  • Its single center point and single radius which are properties of a sphere determine its size.
  • The surface of a sphere is made up of a series of points that are all ‌positioned at the same distance from the center.
  • A sphere is a symmetrical object, hence it looks the same from all angles.

Often used in geometry, spheres have many real-world applications. Some of the areas where spheres find application are, the construction of balls, the design of lenses, globes, and numerous optical equipment. You will also find mentions of spheres in physics, engineering, and many other fields.

Volume of a Sphere

The amount of space occupied by a sphere is the volume of a sphere. The volume of a sphere formula is:

V = (4/3)πr^3

where V is the volume of the sphere, π is the mathematical constant almost equivalent to 3.14159, and r is the sphere radius.

The distance from the center of the sphere to any point on the sphere's surface is called the radius of a sphere.

As an example:

Let us say, we have a sphere with a radius of 5. The sphere volume here would be:

V = (4/3)πr^3 = (4/3)(3.14159)(5^3) = 523.6 cubic units

Therefore, the volume of the sphere here is 523.6 cubic units.

Note: A sphere occupies a three-dimensional space, hence, the volume of a sphere is always measured in cubic units.

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