× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
f
3
b
2
e
2
b
2
j
2
E
2
o
2
L
2
m
2
R
2
C
2
b
2
New Topic  
592257001 592257001
wrote...
Posts: 4
Rep: 0 0
12 years ago
Hi- I need help with a calculus homework problem.  It's an even-numbered problem (not in back of book or solution manual) and is also about a torus, which I have never heard or seen before.  There isn't any other question in the section that resembles this one at all.  

A torus is formed by revolving the graph of (x-1)^2 plus y-squared equals 1.  Find the surface area of the torus.  

How would I do this?  The example in the book talks about the volume of the torus, but not the surface area.  

Thanks for any help!
Read 485 times
1 Reply

Related Topics

Replies
wrote...
12 years ago
A Torus has the form of a donut or innertube. Its cross section is a circle. The circle they gave you is a translation of the unit circle x² + y² = 1 with center (0, 0). This one has the center at (1, 0). I assume they want you to generate a torus by revolving the circle on the x-y plane around the origin. The center of the generating circle would go around in a unit circle itself but totally contained in the z-plane.

The surface element will be the circumference of the generating circle times the surface of a differential radial element (a slice of the donut). By integrating around the unit circle path on the z-plane you will get the total surface.

It seems to me that using a polar coordinate representation of the unit circle on the z plane (i.e. r = 1, &theta &isin [0, 2&pi) you can construct the differential element of the surface in simpler manner.

All the calculus aside, if you look at the problem intuitively, the circumference of the generating circle is 2&pi (it as radius 1). So you are moving a line of length 2&pi around a unit circle in the z plane, which is a length of 2&pi, so the surface should be the product of these two, i.e. 4&pi².
New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  527 People Browsing
Related Images
  
 441
  
 310
  
 134
Your Opinion
Which industry do you think artificial intelligence (AI) will impact the most?
Votes: 486