SOLUTION: The area of a zone is 50.265 sq. cm. if the altitude of the zone is 2 cm, solve the surface area of the sphere.

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Question 1203312: The area of a zone is 50.265 sq. cm. if the altitude of the zone is 2 cm, solve the surface area of the sphere.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

According to Wolfram MathWorld,
https://mathworld.wolfram.com/Zone.html
A zone is like a partial bit of the sphere's surface. We can think of it like a small piece of an orange peel. That link marks the zone in blue.

Here's another article talking about the topic
https://en.wikipedia.org/wiki/Spherical_segment
A spherical segment is a wedge-shaped 3D solid that forms after making those two parallel cuts of the sphere. The zone is then the outer surface area.

On either page is the formula S+=+2%2Api%2AR%2Ah
pi = 3.14 approximately (use more decimal digits of pi to get better accuracy)
R = radius of the sphere
h = height aka altitude
S = surface area of the zone

In this case we are given
S = 50.265
h = 2

We'll use those items to find the radius R.
S+=+2%2Api%2AR%2Ah

50.265+=+2%2A3.14%2AR%2A2

50.265+=+12.56R

R+=+%2850.265%29%2F%2812.56%29

R+=+4.00199045 approximately

Now we can determine the surface area of the sphere
SA+=+4%2Api%2AR%5E2

SA+=+4%2A3.14%2A4.00199045%5E2

SA+=+201.16005

The surface area of the entire sphere is approximately 201.16005 square cm.

In a real life example, this would be the entire orange peel (as opposed to the small piece of it mentioned earlier).