Finding the volume of a spherical sector

In this publication, we will consider a formula with which you can calculate the volume of a sphere sector, as well as an example of solving the problem to demonstrate its application in practice.

Content

Determination of the sector of the ball

Ball sector (or ball sector) is a part consisting of a spherical segment and a cone, the apex of which is the center of the ball, and the base is the base of the corresponding segment. In the figure below, the sector is shaded in orange.

Finding the volume of a spherical sector

  • R is the radius of the ball;
  • r is the radius of the segment and cone base;
  • h – segment height; perpendicular from the center of the base of the segment to a point on the sphere.

Formula for finding the volume of a sphere sector

To find the volume of a spherical sector, it is necessary to know the radius of the sphere and the height of the corresponding segment.

Finding the volume of a spherical sector

Notes:

  • if instead of the radius of the ball (R) given its diameter (d), the latter should be divided by two to find the required radius.
  • π rounded equals 3,14.

Example of a problem

A sphere with a radius of 12 cm is given. Find the volume of a spherical sector if the height of the segment that this sector consists of is 3 cm.

Solution

We apply the formula discussed above, substituting into it the values ​​known under the conditions of the problem:

Finding the volume of a spherical sector

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