A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

Can anyone prove the volume of an ellipse?

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

    Do you mean find an area or actually prove the formula?

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

    LOL can u read it?

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

    yeah i can zoom in. so basically they want you to use calculus to derive the formula for volume of a 3-d ellipse

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

    yes :D

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

    ok, start with equation of ellipse: \[\frac{x^{2}}{b^{2}} +\frac{y^{2}}{a^{2}} = 1\] |dw:1327556444323:dw| then integrate from -b to b, of A(x) which is the area of each circular cross-section where the radius is y: solve the ellipse equation for y \[y = \sqrt{a^{2} - \frac{a^{2}}{b^{2}}x^{2}} = \frac{a}{b}\sqrt{b^{2}-x^{2}}\]

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

    Thanks for ur help :D That was awesome and very clear

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

    wait how did u get that equation

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

    which one?

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

    like from the first to the second

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

    ohhh i get it now

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

    but do i have to integrate it?

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

    or is this the end result?

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

    sorry i skipped some simplifying steps.. no you still have to integrate \[V = \pi \int\limits_{-b}^{b}y^{2} dx\] plug that equation in for y

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

    huh i doubt i will be able to integrate that on my own

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

    ok \[y^{2} = \frac{a^{2}}{b^{2}}(b^{2}-x^{2})\] factor out the constants \[V = \frac{a^{2} \pi}{b^{2}}\int\limits_{-b}^{b} (b^{2} -x^{2}) dx\]

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

    |dw:1327557477105:dw|

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

    yep :)

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

    |dw:1327557564379:dw|

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

    Is that correct?

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

    not quite, you skipped a step first evaluate from -b to b by plugging them in for x

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

    we don't want x in our answer

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

    oh ya whoops lol

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

    |dw:1327557858057:dw|

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

    |dw:1327557996710:dw|

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

    This shld be the answer :D

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

    looks good :) don;t forget about the pi

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

    oh yes thanks for ur help and patience

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

    this is the same way of finding volume of sphere as well just make a =b

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

    ok thanks :D

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

    Goodnight

  31. 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.