Calculating Surface Area of a Torus

In summary, the conversation discusses finding the surface area of a torus generated by rotating a semicircle around different axes. The question is raised whether the surface area would be the same if the semicircle is rotated around x=r instead of y=r. However, it is noted that the resulting surfaces would look different and therefore, the surface areas would not be equal.
  • #1
stonecoldgen
109
0
So the first question is to find the surface area of a torus generated by rotating the circle (or shall I say semi circle) y=√r-x2 around y=r

if the idea is to find the surface are of the half torus and then multiply by 2, wouldn't it be the same for the circle (or shall I say semi circle, again) rotated around x=r?


Thanks.
 
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  • #2
No, I don't think so. If you rotate the same semicircle around the two different axes the surfaces look pretty different, don't they? One looks like the upper half of a full torus, the other looks like the inner half of a full torus. Don't think they are equal in area.
 

1. What is a torus?

A torus is a geometric shape that resembles a donut or ring. It is a 3-dimensional object with a circular cross-section and a hollow center.

2. How is the surface area of a torus calculated?

The formula for calculating the surface area of a torus is 4π²rR, where r is the radius of the circular cross-section and R is the distance from the center of the cross-section to the center of the torus.

3. What is the difference between a torus and a cylinder?

While both torus and cylinder have circular cross-sections, a torus has a constant curvature and a hollow center, while a cylinder has a constant diameter and a solid center.

4. Can the surface area of a torus be measured in any unit of measurement?

Yes, the surface area of a torus can be measured in any unit of length, such as centimeters, meters, or inches.

5. What are some real-life examples of torus shapes?

Some real-life examples of torus shapes include tires, hula hoops, and bagels. It can also be seen in architecture, such as the dome of the US Capitol building.

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