Hello,
Problem:
I can't find my mistake when solving the surface area of a sphere.
Description of the sphere:
Given a sphere of radius centered at the origin. There is a circle at distance from the origin which has a radius of which is inscribed in the sphere
Description of the problem:
I was solving both the volume and area of a sphere. At first I calculated the volume of the sphere in the following approach:
(Area of the circle)
Where it calculates the area of every circle and multiplicates by the differential. No problems here.
Now I wanted to do the same for the surface area, but using the circumference length instead, therefore:
(Length of the circumference)
Ok, I saw in that page a formula on how to calculate the arc length using integration. That could be a way to calculate the lenght of a circumference in the sphere, but still I don't see how that apply to this problem. I am not trying to apply that formula or the one you gave me, I would like to do it purely geometric.
And does it hold or not that is a differential area in the sphere?
No no, I meant I am using the same logic.
One can use use the sum of the areas of disks to calculate the full volume of a sphere,
So I would like to use the sum of the length of circumferences to calculate the area of the surface, but this does not work, and this is where I don't know what is wrong.