Volume of Solid of Revolution Question

In summary, the problem asks to find the volume of a solid rotated 360 degrees around the Y axis given the equation y= -(x/6) + b. However, without any given limits or value for b, the problem is not solvable. The general formula for finding this volume requires limits and a known function for y. It is recommended to clarify with the professor for any missing information.
  • #1
reybob
5
0

Homework Statement



y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis


Homework Equations



If I were given the interval at which I needed to find the volume and/or the value of B I could easily do this using the formula:

[pi] Integrate: (R(y))2 dx


The Attempt at a Solution



What I am trying to ascertain is whether or not this problem is even doable. I don't know if my professor intentionally left out the interval and b value and wants us to do it algebraically but I can't move ahead as most of the questions are based off this one. Please help!
 
Physics news on Phys.org
  • #2
The general formula for this is given by:
[tex]
V=\pi\int_{a}^{b}y^{2}(x)dx
[/tex]
 
  • #3
is it possible to do this question without being given the bounds or knowing where the line sits? Because there is no y intercept and I'm not too sure how you would find the volume without enough information to get the area of the original shape
 
  • #4
welcome to pf!

hi reybob! welcome to pf! :smile:
reybob said:
y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis
…
What I am trying to ascertain is whether or not this problem is even doable.

no, without limits it makes no sense :redface:
 
  • #5
reybob said:

Homework Statement



y= -(x/6) + b, find the volume as this solid is rotated 360 degrees around the Y axis


Homework Equations



If I were given the interval at which I needed to find the volume and/or the value of B I could easily do this using the formula:

[pi] Integrate: (R(y))2 dx

Of course, you mean dy.

You could make up your own x or y limits of c and d and leave your answer as a function of c, d, and b. Better might be to ask the prof if he forgot to include limits.
 
  • #6
Yeah I think I'm going to have to do that. Thank you so much for all this help, this forum rocks!
 

1. What is the definition of volume of solid of revolution?

The volume of solid of revolution is the measure of space occupied by a three-dimensional solid that is formed by rotating a two-dimensional shape around an axis. This shape can be any curve or region bounded by a curve.

2. How do you calculate the volume of solid of revolution?

To calculate the volume of solid of revolution, you can use the disk method or the shell method. For the disk method, you need to integrate the area of cross sections perpendicular to the axis of revolution. For the shell method, you need to integrate the circumference of the shell multiplied by its height.

3. What is the difference between the disk method and the shell method?

The disk method involves using circular cross sections to find the volume, while the shell method uses cylindrical shells. The disk method is best suited for shapes with a circular cross section, while the shell method is more suitable for shapes with a rectangular or square cross section.

4. Can the volume of solid of revolution be negative?

No, the volume of solid of revolution cannot be negative. It is a measure of the amount of space occupied by a solid object, and therefore, it can only have a positive value. If the result of the calculation is negative, it means that the solid does not exist, or the calculation was done incorrectly.

5. In what real-life situations is the concept of volume of solid of revolution used?

The concept of volume of solid of revolution is used in many real-life situations, such as calculating the volume of a water tank, determining the amount of material needed to create a cylindrical or conical shape, and finding the volume of a fruit or vegetable when it is sliced. It is also used in engineering, architecture, and physics to calculate the volume of various objects and structures.

Similar threads

Volume of a solid of revolution around the y-axis (def. integration)
    • Calculus and Beyond Homework Help
Replies
3
Views
957
Volume of a solid of rotation, obtained rotating a function around x=2
    • Calculus and Beyond Homework Help
Replies
2
Views
864
Calculating the volume of the solid in this graph
    • Calculus and Beyond Homework Help
Replies
4
Views
942
Volume of revolution, region bounded by two functions
    • Calculus and Beyond Homework Help
Replies
1
Views
907
I Volume of Solid of Revolution (About the line y = x)
    • General Math
Replies
6
Views
1K
Volume of revolution in the first quadrant?
    • Calculus and Beyond Homework Help
Replies
3
Views
2K
How to find the volume when solids intersect?
    • Calculus and Beyond Homework Help
Replies
8
Views
3K
Solid generated by revolving region, find the diameter of the hole
    • Calculus and Beyond Homework Help
Replies
1
Views
908
Volume of revolution around the y-axis
    • Calculus and Beyond Homework Help
Replies
20
Views
2K
Volume of Revolution: Find V with Shell Method
    • Calculus and Beyond Homework Help
Replies
13
Views
1K

Hot Threads

Recent Insights

Back
Top