A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 5 years ago

Please solve this discs problem: Let R be the region bounded by the graphs of y=1/ sqroot of x,x=3.5 , and y= 4.6. Find the volume generated when region R is rotated about the vertical line x=3.5. (anwser at least three places after the decimal)

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

    My approach is this: you can only do this kind of volume problem by rotating around the x-axis or the y-axis. Since they gave you an "off-axis" rotation, begin by moving the given axis TO the y-axis (since the axis is vertical). That's a move of 3.5 units to the left. A move of 3.5 units to the left is accomplished by subtracting -3.5 from x wherever we find x. In this case, y=1/sqrt(x) becomes y=1/sqrt(x+3.5) and x=3.5 becomes x+3.5 = 3.5 or x=0. Moving the axis of rotation, and then moving all of the boundaries, gives you new equations but a simpler problem. You're now rotating a region about the y-axis. The volume of a disk is pi*r^2*thickness. The r is x (because the disks lie horizontally) and the thickness is dy (same reason). Since we can't mix x's and y's in the integral, solve the y equation for x. That's easily done. Now just plug into the pi*r^2*dy equation to get the thickness of one disk. To finish, integrate what you just created from the bottom y boundary to the top y boundary. I leave it to you to find the boundaries and finish up. The volume of a disk is pi*r^2*thickness.

  2. 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...


  • 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.