Re-derive the surface area of a sphere

[naomineu]

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

 

[fresh_42]

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?

 

[naomineu]

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.

 

[Molar]

Are you looking for this ?
http://mathworld.wolfram.com/SphericalCoordinates.html

https://thecuriousastronomer.wordpress.com/2014/10/21/derivation-of-the-surface-area-of-a-sphere/

See the area element.