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

In summary, the formula for surface area is calculated using spherical coordinates, with the limit of θ from 0 to π. This is due to the convention used for latitude and longitude, where longitude runs from -180 degrees to +180 degrees (or 2π), and latitude runs from -90 degrees to +90 degrees (or π).
  • #1
chetzread
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I found this on the Internet . The formula is
Surface Area = [tex] R^2 \displaystyle \int _0 ^ {2 \pi} \int _{0}^{\pi} \sin \theta d \theta d \phi [/tex]

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...
 

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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.
 
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  • #3
phyzguy said:
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 !
 

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

What is the formula for calculating the surface area of a sphere?

The formula for calculating the surface area of a sphere is 4πr2, where r is the radius of the sphere.

Why is the surface area of a sphere important in science?

The surface area of a sphere is important in science because it is used to calculate properties such as heat transfer, pressure, and radiation absorption. It is also a key component in many mathematical equations and models.

How is the surface area of a sphere related to its volume?

The surface area of a sphere is related to its volume through the formula V = (4/3)πr3, where V is the volume of the sphere. This means that as the radius of a sphere increases, its surface area and volume also increase.

What units are used to measure the surface area of a sphere?

The surface area of a sphere is typically measured in square units, such as square centimeters (cm2) or square meters (m2), depending on the size of the sphere.

How is the surface area of a sphere different from the surface area of other shapes?

The surface area of a sphere is different from other shapes because it is the only shape that has a constant surface area-to-volume ratio. This means that as the size of a sphere increases, its surface area increases at the same rate as its volume, resulting in a consistent ratio between the two.

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