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Thread: Integration to Find Volume of Wine Glass

  1. #1
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    Exclamation Integration to Find Volume of Wine Glass

    Is anyone able to help me with this question?

    Integration to Find Volume of Wine Glass-photo-1.png

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  2. #2
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    Re: Integration to Find Volume of Wine Glass

    Hey siddivi.

    Do you know how to integrate a solid of revolution? Do you know the formulas?

    Also the cylinder has a well known formula for volume and your integration should confirm that.
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  3. #3
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    Re: Integration to Find Volume of Wine Glass

    No I don't, do you know where i can find that?
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  4. #4
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    Re: Integration to Find Volume of Wine Glass

    If you are referring to the volume of a cylinder, imagine a cylinder as a lot of circles stacked on top of one another. You know how to find the area of a circle. Now multiply that by the height of the cylinder.
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  5. #5
    MHF Contributor Matt Westwood's Avatar
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    Re: Integration to Find Volume of Wine Glass

    I'm reminded of Edison, who took a graduate engineer into his lab. He asked the engineer to find the volume of a glass bulb. The graduate got out his calipers, and measured the dimensions of the bulb, then measured the thickness of the glass, then estimated the shape of the bulb as an ellipsoid with given axes, then set up a volume integration to do the mathematics. After an hour or two, eventually he came out with an answer: approximately etc. etc. Edison shrugged, filled the bulb with water, poured the water into a measuring glass and got a number which differed somewhat from that of the graduate.
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  6. #6
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    Re: Integration to Find Volume of Wine Glass

    I understand what you are saying Matt but the point of the post was to give the author a way of understanding integration and to use it to find an arbitrary volume.
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  7. #7
    MHF Contributor Matt Westwood's Avatar
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    Re: Integration to Find Volume of Wine Glass

    Quote Originally Posted by chiro View Post
    I understand what you are saying Matt but the point of the post was to give the author a way of understanding integration and to use it to find an arbitrary volume.
    I know. It was a lighthearted aside. I apologise if it is inappropriate to make such comments.
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  8. #8
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    Re: Integration to Find Volume of Wine Glass

    No worries bro.
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