Volume of Revolution: Solve Assignment Question

In summary, the conversation is about finding the volume of a solid by revolving a region R around the x-axis. The initial solution of using the integral of pi R^2 dx is incorrect and the participants suspect that R is a function of x. The question is clarified and it is revealed that R is actually an area, not a function. Further discussion is had about the correct formula for finding the volume in this scenario.
  • #1
ductape
18
0
The question I need to solve for an assignment is as follows:
Find the volume of the solid that is obtained by revolving the region R around the x-axis.

I figured that the volume would just be the integral of pi R^2 dx, so that would just be pi R^2 x, but that is not the answer. I suspect I am misinterpreting the question.
 
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  • #2
Well, R is probably a function of x. If you write the question, as stated, then we'll be more able to help you!
 
  • #3
My problem is that that is the problem as stated. It doesn't give a function in terms of x.
 
  • #4
Ah nevermind, I found out that the question was referring to an area already found in a previous question.
 
  • #5
Yes, and if it didn't specify the function, it would be [tex]\pi\int^b_a R^2 dx[/tex] anyway, where R is the closed interval (a,b).
 
  • #6
Even that wouldn't make sense! If R is an interval it is not a number! I think both you and ductape are confusing the interval R with "radius" R.
 

1. What is volume of revolution?

The volume of revolution is a mathematical concept that involves finding the volume of a three-dimensional object created by rotating a two-dimensional shape around a specific axis.

2. How do you calculate volume of revolution?

The volume of revolution can be calculated using the formula V = π∫(f(x))^2 dx, where f(x) is the function that represents the two-dimensional shape and the integral is taken over the desired interval of rotation.

3. What is the difference between disk and washer method in finding volume of revolution?

The disk method involves slicing the two-dimensional shape into infinitesimally small disks and adding up their volumes, while the washer method involves subtracting the volume of the hole in the center of the shape from the volume of the larger shape created by rotation.

4. Can you explain the concept of shell method in finding volume of revolution?

The shell method is another approach to finding the volume of revolution that involves slicing the shape into infinitesimally thin cylindrical shells and adding up their volumes. This method is often used when the shape is better represented by a function in terms of y instead of x.

5. What are some common applications of volume of revolution in real life?

The concept of volume of revolution has many applications in fields such as engineering, physics, and architecture. Some examples include calculating the volume of a water tank, determining the volume of material needed to create a specific shape, and finding the volume of a 3D object created by rotating a 2D design in industrial manufacturing.

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