Why is the limit of θ from 0 to π in the formula for surface area of a sphere?

[chetzread]

I found this on the Internet . The formula is
Surface Area = $$R^2 \displaystyle \int _0 ^ {2 \pi} \int _{0}^{\pi} \sin \theta d \theta d \phi$$

I'm wondering why the limit of θ is from 0 to π only ? why not from 0 to 2π ? Because it's a perfect sphere...

 

[phyzguy]

Are you familiar with spherical coordinates? It might help to study them. Think of latitude and longitude on the Earth. Longitude runs from -180 degrees to +180 degrees, so a full 360 degrees or 2π. Latitude however, only runs from -90 degrees to +90 degrees, so only 180 degrees or π. Whether it runs from +90 to -90 or 0 to 180 is a matter of convention.

 

[chetzread]

Are you familiar with spherical coordinates? It might help to study them. Think of latitude and longitude on the Earth. Longitude runs from -180 degrees to +180 degrees, so a full 360 degrees or 2π. Latitude however, only runs from -90 degrees to +90 degrees, so only 180 degrees or π. Whether it runs from +90 to -90 or 0 to 180 is a matter of convention.

thanks , understand now !