Prove volume of a torus equation

[brandy]

how does the formula for volume of a torus work.
is there a proof with integration??

could you use an ellipse?

 

[zhentil]

It's a surface of revolution, so yes, there is a formula (method of cylindrical shells).

 

[tiny-tim]

how does the formula for volume of a torus work.
is there a proof with integration??

Hi brandy!

Yes, slice it into horizontal rings (or vertical discs), and integrate.

could you use an ellipse?

uhhh?

 

[brandy]

by ellipse i mean, an ellipse is revolved around a circular ring.
sort of like taking a torus and stretching it upward...
get me?

 

[brandy]

also what could you use a shape like a polygon or something and revolve it around a circle.

how could you would out the volume?

 

[tiny-tim]

by ellipse i mean, an ellipse is revolved around a circular ring.
sort of like taking a torus and stretching it upward...
get me?

also what could you use a shape like a polygon or something and revolve it around a circle.

how could you would out the volume?

ah! got you!

yes, you can use any cross-section shape …

if you slice it into horizontal rings, you just need to know the width of the polygon at each height …

and if you use vertical discs, you just need to know the height of the polygon at each width

 

[brandy]

sorry. i kept rewording what i was going to say and i didnt read what i wrote.
so all you need is the x,y positions ?
can you explain how this works??
keep in mind i know nothing AT ALL.

 

[brandy]

i mean like wat do u do to the points... to get the volume of revolution

 

[Pjennings]

Have you considered using Pappus' centroid theorem?