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Comments
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.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
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.