A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

blackstreet23

  • one year ago

Let Vx and Vy represent the volumes of the solids that result when the region enclosed by y=3x, y=0, x=1, x=b (b>1) is revolved about the x and y axis, respectively. Is there a value of b such that Vx=Vy?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Region of interest:|dw:1433735228846:dw|

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The solid we get upon revolving about the \(y\) axis: |dw:1433735322750:dw| and the solid we get upon revolving about the \(x\) axis: |dw:1433735432439:dw|

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The volumes of each are given by the integrals \[V_y=2\pi\int_1^bx\times3x\,dx=6\pi\int_1^bx^2\,dx\]and\[V_x=\pi\int_1^b(3x)^2\,dx=9\pi\int_1^b x^2\,dx\]Assuming \(b\) is fixed, what do you think? Hint: Try writing \(V_x\) in terms of \(V_y\), or the other way around.

  4. blackstreet23
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks a lot pal for your help!!!

  5. 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.