Ball

author: Петя
viewed: 1860 times
Българска версия:

• Definition: A ball is the set of points inside a sphere

The centre О and the radius R of a sphere are called centre and radius of a ball

Intersection of a ball with a line that is running trough its centre is called great circle of the ball.

The ball is rotational body that is formed when a semi circle is rotated around its diameter

On interception of the ball with a plane, the two parts that are formed are called ball segments.

A part of a ball that is situated between two parallel planes is called ball layer.

• Definition: Volume of a ball segment is the common limit of two sequences, formed by the volumes of the inscribed and circumscribed bodies which consist of right cyrcular cylinders with equal heights, when the number of these cylinders is infinetely growing
  

    Volume of a ball segment with height h (h<=R) from a ball with radius R is V₀ = (3R – h)пh²/3.

 In that case h = R we calculate the volume V of a semi-ball (sb) with radius R: V_sb = 2пR³/3. The volume of the whole ball with radius R is V = 2V_пк, i.e. V = 4пR³/3