Take a regular torus (doughnut) shaped object and cut a vertical slice through it at line A-A1(Fig1).

Now look at the cross section formed(Fig2). Is it possible to calculate the volume of the original Torus? Prove your results.

The "tube" diametrer = 12mm with a chord 0f 2mm
From this we can calc. that the chord in the outside
circle is 11.92mm in, and we know that it is 50mm long
then tanA =25/11.92
A=64.5
180- 64.5*2 = 51
tan51 = 25/B
B=20.24
20.24+11.92 = 32.16
outer radius = 32.16
32.16 - 12 = 20.16
inner radius = 20.16
Torus volume = 2pisq * radius from center to tube center * tube radius squared

volume = 19.74 * (20.16+6) * 6sq
= 18590 cubic centemeters

Posted by stig on 2004-12-02 18:29:59