Topic: Volume of a Torus
Not finding your answer? Try searching the web for Volume of a Torus
Answers to Common Questions
What is the volume of this torus using integration?
x^2 + y^2 = 1 about the line x = 1 dA = dx * dy d = 2 - x dV = 2π(2 - x) dA = 2π(2 - x) dx dy V = ∫[y= -1 to 1] ∫ [x = -√(1 - y^2) to √(1 - y^2)] 2π(2 - x) dx dy = 8π ∫ √(1 - y^2) dy [y = -1 to 1] = 4π [ y√(1 - y^2) + arcsin(y)] from -1 to ... Read More »
Source: http://answers.yahoo.com/question/index?qid=20110212121759AA4Ie1A
How do you derive the volume of a torus?
Let's take the circle with equation x² + (y - R)² = r² with R > r > 0 and revolve this around the x-axis. This will generate a torus. Solving for y, we obtain y = R ± √(r² - x²). Note that x is in [-r, r]. So, the volume of the torus equals... Read More »
Source: http://answers.yahoo.com/question/index?qid=20110119182745AAgPJns
How to prove volume of a torus using revolution of solids?
Yes, that is the way exactly, but subtract the volumes of the solids, bounded the "outside" and "inside" semicircles. You'll need the formula for the volume of solid of revolution and the following very popular integral: ∫ [-r, r] √(r² - x²... Read More »
Source: http://answers.yahoo.com/question/index?qid=20100126081137AAtyjMp
More Common Questions
Answers to Other Common Questions
Think of a torus as a circular disc being swung around a center point. So you have a two-dimensional area (of the disc) being moved through the third dimension thus sweeping out a volume. The three dimensional volume has the shape of a doug...
Read More »
Source: http://answers.yahoo.com/question/index?qid=20111030165829AASJhgG
Let R be the distance from the centre of the tube to the centre of the torus, and let r be the radius of the tube. Then, the volume of the torus is equal to 2*pi^2*r^2*R. Similarly, the surface area of a torus is given by 4*pi^2*R*r.
Read More »
Source: http://snippets.com/in-calculus-how-do-i-find-the-volume-of-a-tor...
