- #1
Calculating the Surface Area of a Sphere: How Does it Differ?
- I
- Thread starter AyoubEd
- Start date
-
- Tags
- Area Differential Sphere
In summary, the conversation discusses the formula for calculating the area of a circular band on a sphere in spherical coordinates. The formula is dA = R^2 sinθdθdφ and when R is set to 1, the result is Aring = 2πsinθdθ. The conversation also includes a helpful image for visualizing the concept.
- #2
wrobel
Science Advisor
- 1,104
- 961
I also have not got it . Area on two dimensional manifold is a 2-form not 1-form
- #3
AyoubEd
- 10
- 2
it's confusing and wasting my time 
.
thank you anyway.
.thank you anyway.
- #4
nasu
Homework Helper
- 4,441
- 894
The formula represents the area of a circular band on the sphere.
Like the shaded area in this image
http://www.mathalino.com/sites/default/files/images/001-total-surface-sphere-integration.jpg
In general is dA=R2sinθdθ but in that text they say that R=1.
Like the shaded area in this image
http://www.mathalino.com/sites/default/files/images/001-total-surface-sphere-integration.jpg
In general is dA=R2sinθdθ but in that text they say that R=1.
- #5
jedishrfu
Mentor
- 15,051
- 9,571
Yes Nasu has got it right, the differential area of a sphere in spherical coordinates is:
##dA = R^2 sin \theta d\theta d\phi##
and integrating over ##d\phi##
and then setting R=1 you get
##Aring = 2\pi * sin \theta d\theta##
##dA = R^2 sin \theta d\theta d\phi##
and integrating over ##d\phi##
and then setting R=1 you get
##Aring = 2\pi * sin \theta d\theta##
- #6
AyoubEd
- 10
- 2
Thanks a lot guys.
that was very helpful
that was very helpful
FAQ: Calculating the Surface Area of a Sphere: How Does it Differ?
What is the differential area of a sphere?
The differential area of a sphere is the infinitesimal surface area of a small element on the surface of a sphere. It is the amount of area that would be covered by an infinitesimally small patch on the surface of the sphere.
How is the differential area of a sphere calculated?
The differential area of a sphere is calculated using the formula dA = r^2 sin(theta) dθ dφ, where r is the radius of the sphere, theta is the angle measured from the polar axis, and phi is the angle measured from the equatorial plane.
Why is the differential area of a sphere important?
The differential area of a sphere is important in many fields of science, including physics, mathematics, and engineering. It is used in calculations involving surface integrals, spherical coordinates, and differential geometry.
How does the differential area of a sphere change with respect to the radius?
The differential area of a sphere is directly proportional to the square of the radius. This means that as the radius increases, the differential area also increases, and as the radius decreases, the differential area decreases.
Can the differential area of a sphere be negative?
No, the differential area of a sphere cannot be negative. It is a physical quantity that represents the actual surface area of a sphere, which cannot be negative. The differential area is always a positive value.