Spherical Zone

Zone
A zone is that portion of the surface of the sphere included between two parallel planes.
 

Spherical zone of one base and two bases

 

Properties of Spherical Zone

  • The bases of the zone are the circumference of the sections made by the two parallel planes.
  • The altitude of the zone is the perpendicular distance between these two parallel planes.
  • If one of the bounding parallel planes is tangent to the sphere, the surface bounded is a zone of one base.

 

Area of the Zone
The area of any zone (one base or two bases) is equal to the product of its altitude h and the circumference of the great circle of the sphere.

$A_{zone} = \text{circumference of great circle } \times \text{ altitude}$

$A_{zone} = 2\pi Rh$

Note that when h = 2R, the area of the zone will equal to the total surface area of the sphere which is 4πR2.
 

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