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Thread: Just a Simple* Math Question

  1. #1
    Senior Member Senior Member naut's Avatar
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    Default Just a Simple* Math Question

    *Simple is subjective

    I've got this question for maths; but I can't get the equation which I have to integrate:

    A drinking glass has a shape of a truncated cone. If the internal radii of the base and the top are 3cm and 4cm respectively and the depth is 10cm, find by integration, its capacity. If the glass is filled with water to a depth of 5cm, find the volume of the water.

    Anybody know how to deduce an equation from this question?
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    Default Re: Just a Simple* Math Question

    Well I remember those problems were annoying if that's any consolation. Let's see, by integrating what you are doing is taking a really small slice with the area of the base, and than another and so on infinitely many times which gives you an approximation of the volume. Soooo I don't remember the details. You'll probably have 3 and 4 on the little squiggly thing.

  3. #3
    Senior Member Senior Member naut's Avatar
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    Default Re: Just a Simple* Math Question

    Thanks for clearing that up for me.
    #Hillary4prism

    BD:TW

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    Default Re: Just a Simple* Math Question

    Maybe c is 10?

    Maybe you take the formula for volume of a cone and do some calculus thing to it and put 3 and 4 and 10 in their somehow? Man I don't remember calculus.

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    Thread killer Member Rodion Romanovich's Avatar
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    Default Re: Just a Simple* Math Question

    Under construction...

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    Senior Member Senior Member naut's Avatar
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    Default Re: Just a Simple* Math Question

    Edit: I know how to integrate and find volume using integration.
    Last edited by naut; 05-01-2007 at 09:25.
    #Hillary4prism

    BD:TW

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    Master of useless knowledge Senior Member Kitten Shooting Champion, Eskiv Champion Ironside's Avatar
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    Default Re: Just a Simple* Math Question

    Create the whole cone and remove the non-existant part.
    4^2*pi*h(40 unless I'm mistaken)/3-3^2*pi*h(30)/3

    3,5^2*pi*h(35)/3-3^2*pi*h(30)/3

    Considering what I just wrote, it seems that it's either a double integral or a triple.

    int: int: int: r/3 drad/dt dr/dt, dh/dt or something like that (i don't think this one handles the cone part correctly).
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    zombologist Senior Member doc_bean's Avatar
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    Default Re: Just a Simple* Math Question

    truncated cone
    They still subject people to these ?

    We saw them in the alst year of HS, never needed to know anything about them again (and I'm an engineer).

    What i think:

    first a formula for the area of a cirkel:

    2 pi int(r dr)

    now integrate it over the height

    2 pi int(int(r dr) dx)

    with dr/dx =0.1 -> dx=10dr

    20 pi int(int(r)dr dr )

    You now have a double integral over r, solving it you get

    20/6 pi r^3 between r=3 and r=4

    calculate that and you should get the volume.

    I checked using the basic cone formulas, it should be correct, i hope this isn't for credit ...
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    Thread killer Member Rodion Romanovich's Avatar
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    Default Re: Just a Simple* Math Question

    Quote Originally Posted by Rythmic
    Edit: I know how to integrate and find volume using integration.
    Equation is 3+0.1x for the line of the side of the cone. Integrate this equation by using the disc solid of revolution method from 0 to 5 for the water-filled 5 cm stuff, and from 0 to 10 for the full capacity. The full equation would be something like:
    pi * INTEGRAL((3+0.1x)^2)dx
    with the integral limits being 0 and 5, and 0 and 10, respectively.

    This should become:
    pi * INTEGRAL0to5 (9 + 0.6x + 0.01x^2) dx =
    pi * (9*5 + 0.3 * 5^2 + 0.01/3* 5^3) =
    pi * (45 + 7.5 + 0.01/3* 125) =
    pi * (52,5 + 1.25/3) =
    pi * 635/12 = approx. 166 cm^3

    I hope I got the calculation right, but I'm not sure
    Last edited by Rodion Romanovich; 05-01-2007 at 11:23.
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    Sovereign Oppressor Member TIE Fighter Shooter Champion, Turkey Shoot Champion, Juggler Champion Kralizec's Avatar
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    Default Re: Just a Simple* Math Question

    Gah!

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    Simulation Monkey Member The_Mark's Avatar
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    Default Re: Just a Simple* Math Question

    Quote Originally Posted by LegioXXXUlpiaVictrix
    Equation is 3+0.1x for the line of the side of the cone. Integrate this equation by using the disc solid of revolution method from 0 to 5 for the water-filled 5 cm stuff, and from 0 to 10 for the full capacity. The full equation would be something like:
    pi * INTEGRAL((3+0.1x)^2)dx
    with the integral limits being 0 and 5, and 0 and 10, respectively.
    Yes. This is how I'd do it. I'll just explain how to get the line of the side of the cone, as it would seem to be your problem with this thing.

    Just think of the cone and take a cross-section of it along the axis and you'll see the line on the cross-section plane. Then, if you think of the cross-section plane as your basic (x,y) plane you can simply regard the question as the usual analytic geometry - find the equation of the line, and after that it's the integration described above. Try drawing a picture of it, pictures are nice. Pictures are your friend.

    Edit. Ahh, it feels good to integrate for a while, even if only schematically. *leaves to integrate happily into the night*

    Edit2. Yes, it's simple. I'd be damned if it was for credit. Where are you studying? We might as well compare educational systems while at it, as well
    Last edited by The_Mark; 05-01-2007 at 12:25.

  12. #12
    Senior Member Senior Member naut's Avatar
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    Default Re: Just a Simple* Math Question

    Thanks for the responses.

    Quote Originally Posted by The_Mark
    find the equation of the line, and after that it's the integration described above.
    ...
    Try drawing a picture of it, pictures are nice.
    I did that using the 2-point formula, and it seems I got the right answer for f(y).

    Picture? This is what I understand it as being (Note just realised it should be (f(y))^2 in the picture):


    Quote Originally Posted by LegioXXXUlpiaVictrix
    Equation is 3+0.1x for the line of the side of the cone.
    ...
    pi * INTEGRAL0to5 (9 + 0.6x + 0.01x^2) dx =
    Ok I got that using the 2-point formula; I also got the step before integration right. So that must mean my integration was wrong.

    Quote Originally Posted by LegioXXXUlpiaVictrix
    = pi * 635/12

    I hope I got the calculation right, but I'm not sure
    That's the answer.

    Quote Originally Posted by The_Mark
    i hope this isn't for credit
    Quote Originally Posted by doc_bean
    I'd be damned if it was for credit
    I'm a high-school student. What's credit?

    Edit:
    Quote Originally Posted by Fenring
    Gah!
    Seconded.
    Last edited by naut; 05-01-2007 at 12:44.
    #Hillary4prism

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    Cynic Senior Member sapi's Avatar
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    Default Re: Just a Simple* Math Question

    I'm a high-school student. What's credit?
    An american terminology
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    Default Re: Just a Simple* Math Question

    *walks into thread*
    *dies*

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    Senior Member Senior Member naut's Avatar
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    Default Re: Just a Simple* Math Question

    @ Stig:

    Thanks for the working LegioXXXUlpiaVictrix, I know exactly what I did wrong now. When integrating I divided the constant and the index wrongly. ()

    Quote Originally Posted by The_Mark
    We might as well compare educational systems while at it
    I take it you do this stuff at Uni then? I've got to do it at school, quite irritating really. And questions like these are pretty common in our assessments. The hardest one I've ever got was:

    A hemispherical bowl of radius a units is filled with water to a depth of a/2 units. Find, by integration, the volume of the water.

    The teacher couldn't even do it, I'm proud to say that it took me under 5 minutes to do it.
    #Hillary4prism

    BD:TW

    Some piously affirm: "The truth is such and such. I know! I see!"
    And hold that everything depends upon having the “right” religion.
    But when one really knows, one has no need of religion. - Mahavyuha Sutra

    Freedom necessarily involves risk. - Alan Watts

  16. #16

    Default Re: Just a Simple* Math Question

    This thread is enough to fry my dyslexic brain into oblivion...

    I am glad I'm not studying what Rythmic is, in my day it was:

    "A man has five camels, he trades two of these for another man's 45 year old spinster sister, besides being totally ripped off, how many camels does he have left?"

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    Enlightened Despot Member Vladimir's Avatar
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    Default Re: Just a Simple* Math Question

    I took all the advanced courses I could in High School and I just realized that all of that information is just gone. What's pie?


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  18. #18
    Senior Member Senior Member naut's Avatar
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    Default Re: Just a Simple* Math Question

    Quote Originally Posted by Vladimir
    advanced courses I could in High School
    Here in NSW we have the following levels of Math:

    General - Basic, such as algebra, probability and statistics
    2 Unit (which is what I'm doing) - Relatively difficult, the hardest stuff we do is application of calculus and the trigonometric functions
    3 Unit (which I used to do) - Basically they do the 2 Unit course but very quickly and then do 5-6 more topics on top of that.
    4 Unit - Simply put death.
    #Hillary4prism

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    Some piously affirm: "The truth is such and such. I know! I see!"
    And hold that everything depends upon having the “right” religion.
    But when one really knows, one has no need of religion. - Mahavyuha Sutra

    Freedom necessarily involves risk. - Alan Watts

  19. #19
    Simulation Monkey Member The_Mark's Avatar
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    Default Re: Just a Simple* Math Question

    Quote Originally Posted by Rythmic
    I take it you do this stuff at Uni then? I've got to do it at school, quite irritating really. And questions like these are pretty common in our assessments. The hardest one I've ever got was:

    A hemispherical bowl of radius a units is filled with water to a depth of a/2 units. Find, by integration, the volume of the water.

    The teacher couldn't even do it, I'm proud to say that it took me under 5 minutes to do it.
    Naw, I'm just about to graduate from the Finnish equivalent of high school; finished my matriculation exams this March and I'm hoping for a sizeable scholarship for a full 60/60 score from maths

    The bowl assignment doesn't sound that difficult.I'm just screwing something obvious up right now with it. Gah. Lack of routine is not your friend

    I'm a high-school student. What's credit?
    I don't know, it's American and probably something about getting bonus points from doing some voluntary and/or hard assignments.

  20. #20
    Member Member Avicenna's Avatar
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    Default Re: Just a Simple* Math Question

    Forcing you to do it by integration is evil.

    Easy way out is find the volume of the cone and subtract the cut off top bit.
    Student by day, bacon-eating narwhal by night (specifically midnight)

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    Senior Member Senior Member naut's Avatar
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    Default Re: Just a Simple* Math Question

    Quote Originally Posted by The_Mark
    I'm just about to graduate from the Finnish equivalent of high school
    I hope the you get the results you wanted. I've got half a year left of my schooling.

    Quote Originally Posted by The_Mark
    The bowl assignment doesn't sound that difficult.
    It's just a bit confusing.
    V = π∫ a/2 to a (a^2 - y^2) dy
    = π [(a)^3/3 - (y)^3/3] a/2 to a
    = π/3 {a^3 - (3(a)^3)/8 - a^3 + (8(a)^3)/8}
    = π/3 {(5(a)^3)/8}
    = (5π(a)^3)/24

    Quote Originally Posted by Avicenna
    Forcing you to do it by integration is evil.
    But strangely satisfying if you get it right.
    #Hillary4prism

    BD:TW

    Some piously affirm: "The truth is such and such. I know! I see!"
    And hold that everything depends upon having the “right” religion.
    But when one really knows, one has no need of religion. - Mahavyuha Sutra

    Freedom necessarily involves risk. - Alan Watts

  22. #22

    Default Re: Just a Simple* Math Question

    Quote Originally Posted by Cambyses II
    This thread is enough to fry my dyslexic brain into oblivion...

    I am glad I'm not studying what Rythmic is, in my day it was:

    "A man has five camels, he trades two of these for another man's 45 year old spinster sister, besides being totally ripped off, how many camels does he have left?"

    4 if you count the sister


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  23. #23
    Simulation Monkey Member The_Mark's Avatar
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    Default Re: Just a Simple* Math Question

    Quote Originally Posted by Rythmic
    I hope the you get the results you wanted. I've got half a year left of my schooling.
    Yep, thanks, I got quite what I wanted; I can pretty much walk into whatever physics/maths uni in Finland

    Good luck with your last days, enjoy them
    But strangely satisfying if you get it right.
    That's true. The wonders of maths...

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