The volume of a sphere does NOT equal , it's .
Lesson EASY PROOF of volume of a sphere
I don't know if this should be in Geometry or in Calculus since I've since quite a lot of derivations using calculus.
I've always wondered how the Vol. of the Sphere = (4/3)(pi)(r^3) [I'm sorry I put 4(pi)(r^2)]
So can I use steradians to prove it?
So here's my way:
The volume of a cone (I'm thinking that a steradian is a cone with a curved base) = 1/3(Are of the Base)(height)
And there are 4 steradians in a sphere so
=(4/3)(pi)(r^2)(r) since the vertex of a steradian is at the center of the circle
Is this correct?
Okay so I can't edit my first post so I'm gonna reply here.
I know that the SA of a sphere is 4(pi)(r^2) by steradians
A steradian has a SA of (r^2) where r is the radius of the given sphere and there are 4(pi) number of steradians in a sphere.
So I've got the volume of the sphere but I can't explain it.
where the cone has a sort of distorted base with its vertex at the centre of the circle. and with that in mind, its height is the radius of the sphere.
So substituting the stuff,
where r is the radius of the circle, and R is the radius of the sphere.
P.S. Please don't use calculus. I want to explain it to others as simple as possible. And I can't understand calculus.
It makes sense, but I can't explain it.