A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

water is running out a conical funnel at the rate of 1cu in per sec. if the radius of the base of the funnel is 4an and the altitude is 8in. find the rate at which the water level is dropping when it is 2 in from the top.

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    change of rates eh....

  2. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    v' = 1 ft^3 per sec; or simply 1 the rate of h is what we wanna determine

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    volume of a cone = (1/3)(base area)(height)

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the relation of height to raduis is given by the cross section of the cone

  5. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    h = -2r+8 right?

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

    can you show the solution?

  7. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    v = (1/3)(pi 2^2)(-2r +8)

  8. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im working on it; havent got to the end yet lol

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    pi 2^2 was meant to be pi r^2

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lets re work that with h as the variabe so we can see the rate of change with respect to h and not r

  11. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    r = (h-8)/-2 or (8-h)/2

  12. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    v = (1/3)(pi ((8-h)/2)^2)(h) perhaps?

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[v = \frac{h}{3}*\frac{\pi.(8-h)^2}{4}\]

  14. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    64hpi +h^3pi -16h^2pi --------------------- = v derive now 12

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    64pi +3h^2pi -32hpi --------------------- = v' derive now 12

  16. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    pi(64 +3h^2 -32h) = 12 64 +3h^2 -32h = 12/pi right?

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

    ang gulo wah

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe i mess that up alittle dv/dh = that up there dv/dt = 1 and dv/dh dh/dt = dv/dt

  19. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we wanna find dh/dt sooo dh/dt = dh/dv dv/dt ; gotta take the inverse if thats gonna work

  20. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dh/dt is the inverse of dh/dv right :)

  21. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    on paper i get dh/dt = -1/(9pi)

  22. 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.