Volume of the Sphere

• Aug 2nd 2012, 04:05 AM
Volle
Volume of the 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[(1/3)(2)(pi)(r^2)(h)]
=(4/3)(pi)(r^2)(r) since the vertex of a steradian is at the center of the circle
=(4/3)(pi)(r^3)

Is this correct?
• Aug 2nd 2012, 04:30 AM
Prove It
Re: Volume of the Sphere
The volume of a sphere does NOT equal \displaystyle \begin{align*} 4\pi r^2 \end{align*}, it's \displaystyle \begin{align*} \frac{4}{3}\pi r^3 \end{align*}.

Lesson EASY PROOF of volume of a sphere
• Aug 5th 2012, 03:30 AM
Volle
Re: Volume of the Sphere
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.
([V{cone}][SA{sphere}])/Area{circle}

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,
[(1/3)(pi)(r^2)(h)][4(pi)(R^2)]/(pi)(r^2)
=[(1/3)(pi)(r^2)(R)][4(pi)(R^2)]/(pi)(r^2)

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.
Someone help...
• Aug 5th 2012, 07:40 AM
skeeter
Re: Volume of the Sphere
what is wrong with the link provided by Prove it ? the proof shown there does not involve calculus.
• Aug 6th 2012, 03:37 AM
Volle
Re: Volume of the Sphere
No, what I'm asking is, is my proof correct? And can you help on the explaining?