I would fill a measuring cup and see how much I need to pour in to fill the wine glass 😛
But if you want to use math for some reason, you can take a triple integral in polar co-ordinates or do some tricks to simplify it down to a 2 dimensional problem.
At any rate, seems how you have no upper limit for y, the volume will be infinite as parabolas go on forever.
BigBoy on November 30th, -0001
Who in their right mind would take a cross section of a wine glass to find its volume? Isn’t the glass useless now?
Fill it with water and pour it out into a graduated cylinder.
Gothicbunny on November 30th, -0001
We will assume that the wine glass is round and that the height of the wine glass is h (the distance from the bottom of the parabola to the top of the glass).
Set up an element of volume and then integrate. The element will be cylindrical, perpendicular to the y-axis and have a thickness of dy. The radius of the element will be x, the distance from the y-axis to the side of the glass. It will then be integrated from y=0 to y=h.
dV = pi^x^2 dy = pi(0.25y^4)dy
Integrate to get: Volume = (1/20)pi*y^5 evaluated from y=0 to y=h
Volume = (pi/20)h^5
I forgot to mention, you need the height for a definite volume. Just plug it into the equation above and you willhave your volume.
Do a quick check (assuming a height).
Lets take a big wine glass and make h=4 so max radius is 8.
The volume of a cone that encloses the wine glass is pi*r^3*h/3. So volume = pi*8^2*4/3 = 268
So the volume of the wine glass must be less than this.
Volume of glass = (pi/20)4*5 = (pi/20)1024 = 160.85
Rizal on August 30th, 2014
Lovely to meet you (finally) today !! Your stand was by far the most colourful there. So sorry I didn’t get back to see you …. I just ran out of time and had a long drive home. Will catch up in a colpue of weeks time. Enjoy the rest of the show and I hope it’s really successful for you xxx
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Mayumi
on November 30th, -0001
I would fill a measuring cup and see how much I need to pour in to fill the wine glass 😛
But if you want to use math for some reason, you can take a triple integral in polar co-ordinates or do some tricks to simplify it down to a 2 dimensional problem.
At any rate, seems how you have no upper limit for y, the volume will be infinite as parabolas go on forever.
BigBoy
on November 30th, -0001
Who in their right mind would take a cross section of a wine glass to find its volume? Isn’t the glass useless now?
Fill it with water and pour it out into a graduated cylinder.
Gothicbunny
on November 30th, -0001
We will assume that the wine glass is round and that the height of the wine glass is h (the distance from the bottom of the parabola to the top of the glass).
Set up an element of volume and then integrate. The element will be cylindrical, perpendicular to the y-axis and have a thickness of dy. The radius of the element will be x, the distance from the y-axis to the side of the glass. It will then be integrated from y=0 to y=h.
dV = pi^x^2 dy = pi(0.25y^4)dy
Integrate to get: Volume = (1/20)pi*y^5 evaluated from y=0 to y=h
Volume = (pi/20)h^5
I forgot to mention, you need the height for a definite volume. Just plug it into the equation above and you willhave your volume.
Do a quick check (assuming a height).
Lets take a big wine glass and make h=4 so max radius is 8.
The volume of a cone that encloses the wine glass is pi*r^3*h/3. So volume = pi*8^2*4/3 = 268
So the volume of the wine glass must be less than this.
Volume of glass = (pi/20)4*5 = (pi/20)1024 = 160.85
Rizal
on August 30th, 2014
Lovely to meet you (finally) today !! Your stand was by far the most colourful there. So sorry I didn’t get back to see you …. I just ran out of time and had a long drive home. Will catch up in a colpue of weeks time. Enjoy the rest of the show and I hope it’s really successful for you xxx