Undergrad Partial Surface Area of a Tube

Click For Summary
To calculate the surface area of the exposed section of a buried pipe, the formula for the surface area of a cylinder is used, which is 2 times pi times the radius times the length. In this case, the pipe has a radius of 0.848 m and a length of 1.00 m, resulting in a total surface area of 5.64 m². However, since only a portion of the pipe is exposed, the calculation must account for the angle of exposure, which is suggested to be 92 degrees. The discussion also references a potential arc length measurement, indicated as "1219," which may relate to the exposed section's geometry. Understanding these calculations is essential for accurately determining the surface area of the exposed pipe.
deweyirl
Messages
1
Reaction score
0
Hi all,

I hope this is the correct place to post this.

Below is a section of a pipe. The pipe has a radius of 0.848 m.

For this example, assume the pipe is buried below ground but a section of it remains exposed. The centre of the pipe is buried 0.590 mbelow the ground. If we assume the pipe is 1.00 m in length, what I am wanting to know is, how is the surface area of the exposed pipe calculated?

I know the surface area of the pipe would be 2 times pi times the radius times the length of the pipe.
The total surface area of the pipe would be 5.64 m2.

Thanks in advance
 

Attachments

  • Example.JPG
    Example.JPG
    16.6 KB · Views: 229
Mathematics news on Phys.org
You know the circumference right ##2\pi r^2## ?

and that a circle has 360 degrees but you're only interested in 92 degrees.
 
##-## removed ##-##
 
deweyirl said:
...
The centre of the pipe is buried 0.590 mbelow the ground. If we assume the pipe is 1.00 m in length, what I am wanting to know is, how is the surface area of the exposed pipe calculated?
...
For other cases for which you don't have a tool that can give you the angle, this may help:
https://en.wikipedia.org/wiki/Circular_segment
 
Deweyirl. What is the "1219" number in your drawing? That might be the arc length of the exposed pipe or the side if were to be cut and stretched out to make a square.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 5 ·
Replies
5
Views
5K
Replies
4
Views
3K
Replies
7
Views
1K
  • · Replies 11 ·
Replies
11
Views
7K
  • · Replies 15 ·
Replies
15
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
10
Views
3K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 4 ·
Replies
4
Views
2K