Re-derive the surface area of a sphere

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Discussion Overview

The discussion revolves around the re-derivation of the formula for the surface area of a sphere, specifically focusing on using polar and azimuthal angles in the derivation process. Participants are seeking assistance with a homework problem that requires a mathematical approach rather than a geometric one.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in finding a derivation of the surface area of a sphere that utilizes polar and azimuthal angles, instead of geometric methods.
  • Another participant suggests checking the Wikipedia page and related links for information.
  • A later reply provides links to external resources that may contain the desired derivation, specifically mentioning the area element in spherical coordinates.

Areas of Agreement / Disagreement

Participants generally agree on the need for a derivation using polar and azimuthal angles, but there is no consensus on the availability of such resources, as one participant indicates they have not found suitable explanations.

Contextual Notes

Participants have not resolved the issue of finding a derivation that meets the specific criteria of using polar and azimuthal angles, and there may be limitations in the resources available online.

naomineu
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Hey everyone,
I've been stuck on this one piece of HW for days and was hoping someone could help me.
It reads:
The surface area, A, of a sphere with radius R is given by
A=4πR^2
Re-derive this formula and write down the 3 essential steps. This formula is usually derived from a double integral over the polar angle φ and the azimuthal angle θ. Find it on the internet or look it up elsewhere.

I have been searching and a vast majority of the explanations use the geometry to figure it out and I can't find ANY that have an explanation using the polar angle and azimuthal angle.
Can anyone please help?

THANK YOU
 
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naomineu said:
Hey everyone,
I've been stuck on this one piece of HW for days and was hoping someone could help me.
It reads:
The surface area, A, of a sphere with radius R is given by
A=4πR^2
Re-derive this formula and write down the 3 essential steps. This formula is usually derived from a double integral over the polar angle φ and the azimuthal angle θ. Find it on the internet or look it up elsewhere.

I have been searching and a vast majority of the explanations use the geometry to figure it out and I can't find ANY that have an explanation using the polar angle and azimuthal angle.
Can anyone please help?

THANK YOU
Have you looked at the Wikipedia page and the links there?
 
fresh_42 said:
Have you looked at the Wikipedia page and the links there?
I have, but none of the explanations use the polar angle and the azimuthal angle.
 

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