I am really struggling with this math problem for a project I'm working on at work. Anyone???

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Posts: 3545

I am really struggling with this math problem for a project I'm working on at work. Anyone???

Posts: 1769

Uhhh, ummmmm, uhhhhhhhhhhhhhhhhh, uh. Oh wait! Uhhhhhhhhh. Ummmmmm. I am not sure?

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Posts: 8364

in the honor of a recent thread, write that shit in metric system.

and i would just try to formulate a function and solve it by analysing it

and i would just try to formulate a function and solve it by analysing it

in all seriousness, i read that 3 times, 1st time i thought what the fuck is he on about, read it again and thought, this fuckbag has to be kidding, read it once more and decided calling you a fuckbag wasnt good enough - sick-as-aids

Posts: 324

find the volume of cone 3.75 base by 6 height.

take away the volume of cone 2.5 base by 6 height.

now you have volume of the cup.

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

so half the volume of the cup, then do (half volume of cup) = 1/3 base(area) height

Gimme a few more minutes to think about this. Theres a lot of shit going on here.

"lets just say ill nosepress your box if you lipslide my rail ;)" - POWDER.RANGER

Posts: 3545

all i've got so far is

πR(^2)h = volume

(π*3.75)(π*2.5)*6=volume

Now i'm lost

πR(^2)h = volume

(π*3.75)(π*2.5)*6=volume

Now i'm lost

Posts: 324

okay, my fucking head hurts, i give up.

"lets just say ill nosepress your box if you lipslide my rail ;)" - POWDER.RANGER

Posts: 3545

and i actually did the (π * circumference) there.. that's not even right, so..... damnit

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I'll help you give me a few minutes!

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A for effort

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i show you in a minute

in all seriousness, i read that 3 times, 1st time i thought what the fuck is he on about, read it again and thought, this fuckbag has to be kidding, read it once more and decided calling you a fuckbag wasnt good enough - sick-as-aids

Posts: 623

Is 6 inches the height or the actual length of the side?

Posts: 623

Nvm I'm retarded^

Posts: 914

Use this formula to find the total volume
V= pi H/3 (R²+r²+Rr) H is the 6in, R is (3.75/2)in and r is (2.5/2)in.

Than take the total volume divide it by 2

Now with the use the same formula as before and make it equal to the half volume, now you have a formula with 2 unknown variables (H' and R') keep the r as it is (2.5/2)in.

With the triangles you can link the H and R together

you will find something like R' = 1/6 ((R-r) h)-r

Than just replace the result in the formula and you can find the H'

I made this crap http://ladiesfirstchallenge.ch/

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Holy tits

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Posts: 623

H=2.423 approx

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haha if anyone asks if 2.423 is from the top or the bottom of the cup, I will start laughing !!!!

I made this crap http://ladiesfirstchallenge.ch/

Posts: 324

...it can't be, it has to be greater than 3 at least because the cup's wider at the top than the bottom. its going to be closer to 4 than 2.

"lets just say ill nosepress your box if you lipslide my rail ;)" - POWDER.RANGER

Posts: 8186

I would do this by integration. But I don't think it is supposed to be done that way.

there are much better things to do with your life than spend it ruining others. -wh@t

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Skiing is an art form, an escape from all things bad, skiing is perfect, skiing is my obsession.

Love is the amazing shivers you get when you're silently slipping through trees on a powder day, that overwhelming feeling of contentment where your heart beats a little faster and louder. That unmistakable grin of happiness that you can't shake off. It's unconditional, it's unbeatable, it's compassion and it's adventure.

Posts: 623

V= pi H/3 (R²+r²+Rr)

V=pi*6/3((3.75/2)^2+1.25^2+1.25*3.75/2)=46.633 approx

(1/2)*46.633=pi(6-h)/3(1.25^2+1.25r+r^2)

Solve for h

H=something really ugly

Plug the h into:

23.317=pi*h/6(

Son of a bitch I fucked it up

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not only does he take bitchin photos....

Posts: 623

Actual answer

H=3.811 aprox

Posts: 623

But yeah do what jorisblanc said except I solved for r in terms of h and then plugged that into the rs and solved for h.

Posts: 3545

Thanks for all your help guys. We are still working on the paper formula here, but we actually own several of these cups in the office...After several hours of failed math attempts and trying these formulas, we decided to take one cup and fill it to the brim, then empty it into the other cup until they were equal. Our approx. measurement is 3.7inches from the bottom

Posts: 914

You probably could do it by integrating, but I'm pretty sure that the OP has already enough trouble with this problem as it is ;-)

I made this crap http://ladiesfirstchallenge.ch/

Posts: 914

Just wondering, why do you want to find the center volume of a cup ???

I made this crap http://ladiesfirstchallenge.ch/

Posts: 3545

Good question - I had to create a design/theme for some plastic cups we are giving away internally to several departments in the company. We have our company logo on one side, and then I came up with these theme for the reverse :)

Posts: 914

Okay cool !!

I made this crap http://ladiesfirstchallenge.ch/

Posts: 3545

Thanks for the help everyone. + to allllll

Posts: 1395

This is a lot more complicated than it first seems..

I found this nifty website that calculates the volume of a truncated cone..

http://keisan.casio.com/has10/SpecExec.cgi

The site also gives the formulas used in their algorithm. I'm pretty confident that with this information we can find the "midpoint".

In your drawing you say that you have the circumferences of the the two circles that make up the top and bottom of the cup, but i'm assuming that you meant to say diameter because of the way you've drawn your dimensions. If you do actually mean circumference you can easily solve for the radiuses using the formulas:

Circumference = π*d and Radius = d/2

Anyway, back to the actual problem..

When you punch in the dimensions of your cup it stays that the volume is 46.63

Now divide that number by two and and set it equal to the volume formula they provide and sub in all of the information you know..

This gives us an equation that looks like this:

23.31 = (1/3)*π*(R1^2+ R1(1.25) + (1.25)^2)*H

Where:

23.31 is half of the total volume

R1 is the unknown radius of the circle that is the top of the new "half cup"

R2 is the radius of the bottom of the cup

and H is the unknown height.

Now it appears that we cannot solve this for H because we also have R1 as an additional unknown, making 2 unknowns and only one equation. However, because of the cups conical shape, we can relate R1 to H using the principle of similar triangles.

If you look back at the original drawing, we see that the slope of the side of the cup can be described by the difference in the size of the radiuses on it's ends and the total distance over which they change.

Slope = (1.87-1.25)/6

Slope = 0.1 (approximately)

So now that we know the slope we can say that the radius at the middle is just the height at the middle (H) times the slope (.1) plus the radius at the bottom

or written mathematically as..

R1 = .1*(H) + 1.25

Now we can actually solve for H!

Here's the equation I came up with the 2 unknowns..

23.31 = (1/3)*π*(R1^2+ R1(1.25) + (1.25)^2)*H

Now sub (.1*H+1.25) in anywhere R1 appears and we get..

23.31 = (1/3)*π*[(.1*H+1.25)^2 + (.1*H+1.25)*(1.25)+(1.25)^2]*H

^ This is literally a nightmare to try and solve so i'm just gonna use wolframalpha.com

http://www.wolframalpha.com/input/?i=solve+23.31+%3D+%281%2F3%29*%28pi%29*%5B%28.1*H%2B1.25%29%5E2+%2B+%28.1*H%2B1.25%29*%281.25%29%2B%281.25%29%5E2%5D*H+for+H

which says that H = 3.607

I found this nifty website that calculates the volume of a truncated cone..

http://keisan.casio.com/has10/SpecExec.cgi

The site also gives the formulas used in their algorithm. I'm pretty confident that with this information we can find the "midpoint".

In your drawing you say that you have the circumferences of the the two circles that make up the top and bottom of the cup, but i'm assuming that you meant to say diameter because of the way you've drawn your dimensions. If you do actually mean circumference you can easily solve for the radiuses using the formulas:

Circumference = π*d and Radius = d/2

Anyway, back to the actual problem..

When you punch in the dimensions of your cup it stays that the volume is 46.63

Now divide that number by two and and set it equal to the volume formula they provide and sub in all of the information you know..

This gives us an equation that looks like this:

23.31 = (1/3)*π*(R1^2+ R1(1.25) + (1.25)^2)*H

Where:

23.31 is half of the total volume

R1 is the unknown radius of the circle that is the top of the new "half cup"

R2 is the radius of the bottom of the cup

and H is the unknown height.

Now it appears that we cannot solve this for H because we also have R1 as an additional unknown, making 2 unknowns and only one equation. However, because of the cups conical shape, we can relate R1 to H using the principle of similar triangles.

If you look back at the original drawing, we see that the slope of the side of the cup can be described by the difference in the size of the radiuses on it's ends and the total distance over which they change.

Slope = (1.87-1.25)/6

Slope = 0.1 (approximately)

So now that we know the slope we can say that the radius at the middle is just the height at the middle (H) times the slope (.1) plus the radius at the bottom

or written mathematically as..

R1 = .1*(H) + 1.25

Now we can actually solve for H!

Here's the equation I came up with the 2 unknowns..

23.31 = (1/3)*π*(R1^2+ R1(1.25) + (1.25)^2)*H

Now sub (.1*H+1.25) in anywhere R1 appears and we get..

23.31 = (1/3)*π*[(.1*H+1.25)^2 + (.1*H+1.25)*(1.25)+(1.25)^2]*H

^ This is literally a nightmare to try and solve so i'm just gonna use wolframalpha.com

http://www.wolframalpha.com/input/?i=solve+23.31+%3D+%281%2F3%29*%28pi%29*%5B%28.1*H%2B1.25%29%5E2+%2B+%28.1*H%2B1.25%29*%281.25%29%2B%281.25%29%5E2%5D*H+for+H

which says that H = 3.607

Posts: 21133

its actually really easy to get the height of the cone if it were to be continued.

3.75 to 2.5 is a difference of 1.25. so basically, every 1.25 inches the diameter shrinks, it gains 6 inches in length.

at the 3.75 mark it has 0 height

at the 2.5 mark it has 6 height

at the 1.25 mark it has 12 height

at the 0 mark (tip of the cone) it has 18 height

just using a little intuition, you've got a large chunk of the problem down.

now, knowing the total volume of the cylinder (since you have r = 3.75 and h = 18) and the volume of the tip of the cylinder (r = 2.5 and h = 12), you can calculate the volume of the picture shown (which is about 46.64). since the midpoint represents the height at which both volumes are equal, you know that they both have to be at a volume of 23.32.

we know this much already, having barely done any complicated math or setting up equations with variables that will help us determine the height at which the volume of either the top half or the bottom half will be 23.32.

now, it's just a question of doing what ^^ that guy said and solving for the midpoint.

Posts: 528

take the water in the cup and pour it into a box.

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