Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

rainbow22

  • 2 years ago

find the volume of the solid formed by revolving the region bounded by y=x^2, y=0, and x=2 about the y axis

  • This Question is Closed
  1. Thomas9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you know about multivariable calculus perhaps? Or do you want the easy-not-understanding-what-you're-doing way

  2. rainbow22
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The answer is 8pi

  3. rainbow22
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, I am supposed to use the Disk Washer method. I can do it with antiderive(2-y) to get the right answer but I'm pretty sure that's not following th formula I'm given which is outer radius minus inner radius.

  4. Thomas9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Disk Washer?

  5. rainbow22
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    There's a hole in the solid.. so it's called Washer Method.

  6. Thomas9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So how does this method work?

  7. rainbow22
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I do antiderivative from a-b in terms of x or y (y in this case because I rotate about y axis) pi (outer radius)^2 - (inner radius)^2

  8. rainbow22
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{a}^{b} \pi (outer radius)^2 -(innerradius)^2 dx\]

  9. Thomas9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't how that works, I'm afraid.

  10. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1359838432884:dw|

  11. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1359838561883:dw|So let's look at one slice.

  12. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh you're doing the washer/disk method, my mistake.. Lemme slice that differently.

  13. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1359838731527:dw|Ok this type of slice will give us a Disk.

  14. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1359838764034:dw|So we want to get the Volume of this disk.

  15. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The outer radius appears to be the line x=2. And the inner radius our function which is in terms of x, we'll need it in terms of y to integrate since we sliced in the y direction (dy thickness)

  16. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\large y=x^2 \qquad \rightarrow \qquad x=\sqrt y\]

  17. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\large V=\pi\left[(2)^2-(\sqrt y)^2\right]dy\]

  18. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Then to find the total volume in this enclosed area, we Integrate (add up all the slices) from one intersecting point to another. Where do they intersect? Ummm looks like.. y=0 and y=4?

  19. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Simplifying things down gives us, \[\large \pi \int\limits_0^4 4-y \;dy\]

  20. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Imma check my work real quick to make sure I didn't make a mistake somewhere. A little tired, it's possible. lol

  21. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yah I think that's right. Confused about any of that? I went through it a little sloppy D:

  22. rainbow22
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's right. I realize what I did wrong! I had the wrong intersections/points. I did instead from -2 to 2.. not realizing that it was based on terms of y . thank you so much!

  23. zepdrix
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh cool c:

  24. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.