A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

If r=6cm and h=2cm, give or take 0.1cm, which is the expected maximum percentage error in calculating V= pie*(r^2)*h

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

    Apply the propagation of error to the equation of volume. Are you familiar with it?

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

    no

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

    could you show me?

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

    Sure. Actually, for worst case, its a complete differential. My mistake. But here we go. Percent errors come in the form of dr/r, which in our case is .1/6, and dh/h is .1/2. We are looking for dV/V. Do you know any easy way to get to this result?

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

    no, could you go through it quickly all the way to the end please?

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

    Sure. Take the natural log of both sides, giving you: \[lnV = \ln(\pi r ^{2} h) = \ln \pi + 2 \ln r + \ln h\] Can you take the derivative of this?

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

    (1/pie)+(2/r)+(1/h)?

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

    Close. Each variable is subject to change, however.

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

    oh wait is it 2/r?

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

    \[dV/V = 2dr/r + dh/h\] ln pi is a number, so it falls away when a derivative is taken.

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

    Since we are looking for the worst case, you take the absolute value of each term. This doesn't effect this set up at all, however. So we know dr/r and dh/h. So now we plug in and get our answer for dV/V.

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

    so answer is 6%?

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

    2*(.1/6) + (.1/2) = .083333 = 8.33%

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

    ok thank you very much

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

    Anytime. Take care!

  16. 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.