Volume of Solid of Revolution (About the line y = x)

  • I
  • Thread starter PeroK
  • Start date
  • #1
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2021 Award
20,135
11,470
Summary:
Volume of Solid of revolution about unusual axis
I found this problem, which I thought was interesting and somewhat original:

Calculate the volume of the solid of revolution of the area between the line ##y = x## and the parabola ##y = x^2## from ##x = 0## to ##x = 1## when rotated about the axis ##y = x##.
 

Answers and Replies

  • #4
13,324
7,241
I agree just wanted to be helpful here. When I first looked at it, I didn’t know how to tackle it until I saw the older post.

How intractable is it if an arbitrary direction is chosen?
 
  • #5
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2021 Award
20,135
11,470
I agree just wanted to be helpful here. When I first looked at it, I didn’t know how to tackle it until I saw the older post.

How intractable is it if an arbitrary direction is chosen?
It's not particularly hard.
 
  • #6
35,643
7,519
I think the only tricky part is that the thickness of the typical volume element needs to be ds rather than dx; i.e., an increment of arc length along the parabola.
 
  • #7
653
806
Not even that, because the secret to any problem involving a rotated geometric figure is to rotate the co-ordinates ##\mathbf{x}' = \mathsf{R}\mathbf{x}## so that you have it in standard form.
 
  • Like
Likes mfb and jedishrfu

Related Threads on Volume of Solid of Revolution (About the line y = x)

  • Last Post
Replies
10
Views
2K
Replies
1
Views
615
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
3K
I
Replies
9
Views
4K
  • Last Post
Replies
3
Views
8K
  • Last Post
Replies
7
Views
960
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
13
Views
976
Top