Volume of Solid Revolved Around Y-Axis: Bounds Check

In summary, the "Volume of Solid Revolved Around Y-Axis" refers to the volume of a three-dimensional shape created by rotating a two-dimensional shape around the y-axis. To calculate this volume, the formula V = ∫(π * y^2)dx is used, where y is the defining function and dx represents the bounds along the x-axis. A "Bounds Check" is performed to ensure the integration limits and function are accurate. The volume cannot be negative due to the nature of space, and there are limitations to this method, such as only being applicable to certain shapes and requiring a defined function or equation.
  • #1
Saladsamurai
3,020
7
find the volume of the solid resulting when the region enclosed by the curves is revolved around y-axis.

[tex]x=\sqrt{1+y}[/tex] x=0 y=3

I am using this integral...

[tex]V=\int_{-1}^3[\pi(\sqrt{1+y})^2]dy[/tex]

and I am getting the wrong answer.

I think it is just arithmetic, but are my bounds correct?

Thanks,
Casey
 
Last edited:
Physics news on Phys.org
  • #2
Just wondering about the bounds here..
 
  • #3
Your bounds&integral look fine to me.
You should get something like [tex]V=\pi(3+\frac{9}{2}+1-\frac{1}{2})=8\pi[/tex]
 

FAQ: Volume of Solid Revolved Around Y-Axis: Bounds Check

1. What is the meaning of "Volume of Solid Revolved Around Y-Axis"?

The "Volume of Solid Revolved Around Y-Axis" refers to the volume of a three-dimensional shape that is created when a two-dimensional shape is rotated around the y-axis. This is also known as a solid of revolution.

2. How is the volume of a solid revolved around the y-axis calculated?

The volume of a solid revolved around the y-axis is calculated by using the formula V = ∫(π * y^2)dx, where y is the function that defines the shape and dx represents the bounds of the shape along the x-axis.

3. What is the purpose of performing a "Bounds Check" for the volume of a solid revolved around the y-axis?

A "Bounds Check" is performed to ensure that the integration limits (the bounds) are correct and that the function used to calculate the volume is valid for those bounds. This helps to avoid errors and ensures an accurate calculation of the volume.

4. Can the volume of a solid revolved around the y-axis be negative?

No, the volume of a solid revolved around the y-axis cannot be negative. This is because volume is a measure of space and cannot have a negative value. If the calculated volume is negative, it means that there is an error in the integration or the function used.

5. Are there any limitations when using the "Volume of Solid Revolved Around Y-Axis" method?

Yes, there are some limitations when using this method. It is only applicable for shapes that can be rotated around the y-axis, such as circles, semicircles, and parabolas. Additionally, the shape must have a defined function or equation that can be integrated to calculate the volume.

Similar threads

Volume of a solid of revolution around the y-axis (def. integration)
Replies
3
Views
1K
Calculating the volume of the solid in this graph
Replies
4
Views
1K
Triple Integral To Find Volume Between Cylinder And Sphere
Replies
2
Views
124
Solid generated by revolving region, find the diameter of the hole
Replies
1
Views
1K
How Do You Calculate the Volume of a Torus Formed by Revolving a Circle?
Replies
12
Views
4K
Find the volume of the solid bound by the three coordinate planes
Replies
2
Views
824
How to find the volume when solids intersect?
Replies
8
Views
3K
Find the volume using the shell method
Replies
8
Views
2K
Finding Volume of Solid Bounded by Paraboloid and Planes
Replies
2
Views
1K
Find the volume bounded by hyperboloid and plane z = ± d
Replies
14
Views
1K

Hot Threads

Recent Insights

Back
Top