I'm not quite understanding the formation of the radius

In summary, the problem involves finding the volume generated by rotating a region bounded by certain curves about a specified axis. The question is specifically about using the method of cylindrical shells, and the student is unsure about how to find the radius in this particular case. They ask if the radius would be 2-x and wonder why. Another person responds, explaining that since the region is centered around x=2, the cylindrical shells will also be centered around this point and thus the radius will be the distance from (x,0,0) to (2,0,0).
  • #1
Xetman
8
0

Homework Statement


Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves about the specified axis.

y=x^4, y=0, x=1; about x=2

2. The attempt at a solution

I know how to do the problem, except how to find the radius. Like I know if it was about the x-axis then the radius would just be x. But since it's about x=2, would the radius be 2-x? If it is 2-x, why?

I'm guessing it's 2-x because there was a similar problem earlier in the book that showed this being the radius when it was about x=2.
 
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  • #2
Hi Xetman! :smile:

(try using the X2 button just above the Reply box :wink:)
Xetman said:
II know how to do the problem, except how to find the radius. Like I know if it was about the x-axis then the radius would just be x. But since it's about x=2, would the radius be 2-x? If it is 2-x, why?

The region is a sort of collar centred around x = 2.

So your cylindrical shells will also be centred around x = 2 …

so the radius of the shell that goes through (x,0,0) is the distance of (x,0,0) from (2,0,0). :wink:
 

Related to I'm not quite understanding the formation of the radius

1. What is the radius and how is it formed?

The radius is a bone in the forearm, located on the thumb side. It is formed during fetal development through a process called endochondral ossification, where cartilage is gradually replaced by bone tissue.

2. Why is it important to understand the formation of the radius?

Understanding the formation of the radius is important for medical professionals to accurately diagnose and treat any abnormalities or injuries related to this bone. It also provides insight into the evolution of the human body and can aid in the development of new treatments for bone-related conditions.

3. What factors influence the formation of the radius?

The formation of the radius is influenced by genetic factors, as well as environmental factors such as nutrition and physical activity during fetal development. Any disruptions in these factors can lead to abnormalities in the formation of the radius.

4. Can the formation of the radius be affected by external factors after birth?

Yes, the formation of the radius can be affected by external factors after birth, particularly during childhood and adolescence as the bone continues to grow and develop. Poor nutrition, injuries, and certain medical conditions can impact the growth and development of the radius.

5. Are there any common disorders or conditions related to the formation of the radius?

Yes, there are several disorders and conditions related to the formation of the radius, including radial head dislocation, radial head subluxation, and Madelung's deformity. These conditions can cause pain, limited mobility, and other complications, and may require medical treatment.

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