I?m worried about water intoxication, please help me calculate the volume of my drinking glass?
Ok, I weight 128 lbs (5 feet tall), and I should drink 8 glasses full of 8ounces of water. (I make frequent trips to the ladies room and I excercise regularly, but I?m very curious)
But, at work, they have paper cups which are not quite a cylinder shape because the bottom diameter is smaller than the top. My main questions are:
1) How much water is in my 1 paper cup?
2) How many paper cups of water should I drink at work to fulfill at least 8ounces?
Here are the measurements of my glass:
The glass height is 4 inches
The bottom diameter is 2 inches
The top diameter is 3 inches
The glass is 2 cm thick.
I fill my water cup to the rim leaving no room. I spend A LOT of time at work, so there are times that I don?t drink water when I come home, and I just take a shower and go to bed.
NaughtyNinja
on February 8th, 2012
1 US fluid ounce = 29.5735297 ml
Your water cup is a fustrum of a cone. To find its volume we need the height of the imaginary full cone and the height of the imaginary missing cone
x/2 = (x + 4)/3
3x = 2x + 8
x = 8
V = (?/3)(12*1.5^2 – 8*1^2)
V = 19.89675 in^3
V = 19.89675 in^3(2.54 cm/in)^3 = 326.0494 ml
326.0494 ml(1 oz/29.5735297 ml) = 11.02504 oz
64/11.02504 = 5.804967 or about 6 cupfuls
Converting to metric and assuming 2mm thickness (1 mm sounds more reasonable),
V = (?/3)(30.48*3.61^2 – 20.32*2.34^2)
V = 299.4506 ml = 10.125628 oz
64/10.125628 = 6.320596 or about 6 cupfuls
Cocktail
on February 8th, 2012
The notion that you should drink 8 glasses of water is a bit of a misconception, and drinking too much water can actually be a bad thing because it flushes vital electrolytes from your system. A better bit of advice to follow would be “drink 8 glasses of liquid a day”, where liquid can be water, milk, juice, etc.
Anyway, if you’re really concerned with sticking to the 8oz measurement, just fill up one of the paper cups, then dump it out into a measuring cup to see how much it holds.
CheeseCake
on February 8th, 2012
It sounds to me that your cup is approx 4 ounces, which means you need 2 to make 8 ounces.
CrispApple
on February 8th, 2012
Take a cup home and you don’t have to guess. To reduce the risks associated with water toxicity, yes there is such a thing, it is recommended that you should not exceed more than one liter of fluid in an hour.
StarbucksCoffee
on February 8th, 2012
If the sides of the glass are straight (i.e., it gets consistently smaller from top to bottom without any widening then narrowing), then the mean diameter can be used to calculate a rough volume of the glass.
The formula for volume of a cylinder is pi*r*r*height (sorry, I don’t know how to put the mathematical notation here, but it’s pi*radius squared for the area of a cross section, multiplied by the height).
For your glass, the mean diameter is 2.5 inches, and I’m going to assume you mis-stated the thickness of the sides, because I cannot imagine a paper cup with sides that are nearly 1 inch thick (plus, that would leave only a very small opening in the middle).
So…
3.14*1.25*1.25*4=19.625 cubic inches in your glass.
19.625 cubic inches * 0.554 ounces/cubic inch = 10.87 ounces/glass.
Sunburst
on February 8th, 2012
The answer from Snarlsnap is correct. On the Yahoo News on Tuesday was an article exposing health-related myths, including the 8 glasses of water a day. Quote below:
Here’s another myth. “Drink 8 glasses of water a day.” Repovich said people need to replace water lost through breathing, urinating, sweating each day — but that doesn’t necessarily total 64 ounces of water.
“I see an awful lot of people carrying bottled water around,” Repovich said. “I think people are still under the impression that they have to drink 8 glasses of water a day, but most people don’t realize they get water from other sources in the diet.”
And too much water can be harmful, Repovich warned, leading possibly to an imbalance in the body of sodium, a condition called hyponatremia.
There are many imperceptible ways we get water in our diet. Milk is 95% water, so are most other drinks. Steak is 70% water. Most vegetables and fruits are high in water content. The key to life is moderation – including water consumption.
Rick the Pharmacist
Sarah
on February 8th, 2012
You don’t really need to drink 64 oz of water a day. You get water in a lot of other places – in the fruits and vegetables you eat, for example.
It sounds like the volume is about 27 cubic inches. Not sure how many oz that is.
SecretCelebrity
on February 8th, 2012
the cup is 11 ounces
so drink about 6