A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Clarence

  • one year ago

The bass of solid S is the region enclosed by the parabola y = 64 - 25x^2 and the x-axis. Cross-sections perpendicular to the y-axis are squares. Find the volume of the described solid S. Where do I even start?!

  • This Question is Closed
  1. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm on mobile so can't draw but all they're really saying is that the height of the solid z = f(x,y) =64-25x^2 So both width and height of a cross section are driven by the value of x Integrate f(x,y) over the region.

  2. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually no need for double integral. Just create a function A(x) for area at any x and integrate that dx.

  3. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So integrate 64-25x^2? @irishboy123

  4. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(Width = 64-25x^2\) \(Height = 64-25x^2\) \(A(x) = W \cdot H = (64-25x^2)^2\)

  5. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh really? I got area to be \[\frac{ 4(64-x) }{ 25 }\]

  6. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    And then integrating that from 0 to 1 to get 254/25 as my answer?

  7. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry, x was meant to be y, my bad.

  8. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1444053041996:dw|

  9. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I followed my friend's suggestion and had a look at this link: http://slader.com/textbook/9780538498845-stewart-calculus-international-edition-7th-edition/362/exercises/58/

  10. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    drat "perpendicular to" y axis means this..... |dw:1444054108785:dw| \(x = \sqrt{\dfrac{64-y}{25}}\) \(A(y) = \left[ \sqrt{\dfrac{64-y}{25}} \right]^2 \) \(V = \int\limits_{0}^{64} \; \dfrac{64-y}{25} \; dy = \dfrac{2048}{25}\)

  11. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh yeah, that makes sense! Did you accidentally delete your previous reply? :P

  12. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no i thought it had a mistake and i deliberately deleted it and then re-typed it and drew it......again :-) i'm just looking at that web link you produced...........i don't get the 2x part but i'll keep trying.

  13. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Aha, oh okay then :) Me neither to be honest with you, but the next step made sense in my head... Somewhat :p

  14. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks again for your help! Much appreciated :)

  15. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh i see the 2 is because it is both sides of the y axis....

  16. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    which is also the case here...so that factor of 2 goes in as well i did this in my head on mobile and assumed .....wrongly |dw:1444054850625:dw|

  17. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So the answer is actually 8192/25? Go figure :p

  18. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(A(y) = \left[ \color{red} 2 \sqrt{\dfrac{64-y}{25}} \right]^2 = 4 \sqrt{\dfrac{64-y}{25}} \) \(V = \color{red} 4\int\limits_{0}^{64} \; \dfrac{64-y}{25} \; dy = 4 \cdot \dfrac{2048}{25}\)

  19. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[=\dfrac{8192}{25}\]

  20. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sweet, mystery solved!

  21. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you for your patience, have we licked it?!?!

  22. clarence
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think we have! Always a pleasure working with you Mr. Holmes :p :)

  23. IrishBoy123
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you Dr Watson, and vice versa :-))

  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.