A "balloon" of spherical shape is made to a "torus" by tying an axis of it. Which one has more inner pressure?

Question

A torrus shape is similar to a 'tyre', which usually has a measurable inner diameter! The baloon made as torus has 'a zero inner diameter' which is achieved by tying an axis of baloon (with a wire of negligible diameter)!

Both 'spherical baloon' and 'torus baloon' has a concerned inner pressure. Which of these has a higher inner air pressure and why?

Answer 1

i dont think so:...

Answer 2

Well for a sphere to become a torus, by bringing the ends to the middle...and by definition of a torus, the section of which is two perfect circles. the center to center of the two circles in the torus section would have to be one half the sphere diameter. therefore the volume of this torus would be pi^2 * d/2 *d/2 which gives pi^2 * d^2 /4 where d is the original sphere diameter. The volume of the sphere is pi * d^2 so evaluating the constants the torus volume is 2.467 d^2 and the volume of the sphere is 3.14 d^2. So from this we see that the torus has a smaller volume, but the same amount of air as the original sphere balloon, so from this we can conclude that the torus has a higher inner pressure because the air would have to be compressed more to fit into the smaller torus.

Answer 3

The torus baloon has the higher pressure.

You start with a spherical baloon with a given pressure. You then stretch it into a torus by doing work on it. This increases the pressure because pressure is force per unit surface area and you are decreasing the surface area by constraining it at the center of the torus.

Answer 4

If it is done, then the Torus will have higher inner pressure.

Answer 5

A sphere cannot topologically be transformed into a torus.