Actually, the third grade math book might tell you how to calculate the volume of the cylinder, but you don't have enough information to calculate its displacement. Displacement is a measure of weight, not of volume.
But if you know the volume and density of the material to be displaced you can do it.
In a tank of water there is floating a tin tray. On the tray is a glass bottle filled up with water. Someone comes along and upsets the whole arrangement. The glass bottle and the tray are both completely submerged under the water. Does this upsetting of the tray and bottle cause the level of water in the tank, taken at the side of the tank, to go up or to go down ? or does the level remain unchanged?
I thought I was going crazy. Thanks everyone, I did find the answer.
This is true, but in the original problem statement, we weren't given the density.
Wow, that's a cool problem. I'm going to vote for "the level goes down", but I'll admit I had to think on it for a while.
When the pan-bottle system is floating, the weight of the water it displaces is exactly equal to the weight of the floating stuff. That much is obvious.
Because it sinks, it must weigh more than the water it displaces while submerged. Looking at it the other way, the weight of the water it displaces while submerged is less than its own weight.
Since it displaces less water while submerged, the level in the tank must have gone down when it sank. At least I think that's the right answer :-)
Larry, old chap, you're quite wrong. That's the volume for a sphere of diameter D, not a cylinder of circumference C and height [or length] h.
Displacement is an older term, not now used, for volume, since it could be measured by liquid displacement.
That's older than I am; a problem in density ...displacement of water volume equal to ...etc. The clue is to think about the water in the bottle [mass, volume], and to think about what would happen if the bottle was empty.
But if the OP wasn't hosing us when he said he couldn't figure out V, r or h, which is more likely: That he wanted the volume and said displacement? or vice versa?
Displacement, as someone has mentioned is how much of whatever else is moved out of the way by what you have. That's volume. Now if you're looking for density, the common reference is water (SG), where if you know the volume, think EUREKA!
You need not run naked through the streets of Syracuse, however, it's been done.
Bingo! ... you get to collect the cabal dues this month and deduct your 25% handling fee.
;)
Oops, I did give sphere, didn't I? Mea culpa.
That's OK, though. Judging by his response to the proper formula, the OP doesn't have anything CLOSE to a clue anyway. Spoonfeeding time.
- - - - - - - - - - - - - - - - - - Heart Attacks: God's revenge for eating his little animal friends --
Although I grant I made the (perhaps rash) assumption that you could somehow muddle through to find the radius of a circle knowing the circumference...
If that's the root of the problem, then since c = pi*d = 2*pi*r ==> r = c/(2*pi)
From which it follows that
V = pi*[c/(2*pi)]^2*h = c^2*h/(4*pi)
I was raised in an area of Canada known as the Yukon and never saw a school until I was 14. I'm a stone and wood carver and it pays my bills. If I could afford to go to school I would.
Been there ...who hasn't?
Pay no attention. My father had little schooling, but was likely the cleverest man I ever met. It showed in what he did with the schooling he had, and the use of his brain in his trade. You'll find that the smartest people all around are the humblest. They're smart enough to know how little they know in the scheme of things. A good way to reply would be to show some photos of your work in alt.binaries.pictures.woodworking .
Yeah right! Most third graders can't add very well and about 1/2 of them can read the title of the book.
You sure you don't mean a math book for the third year of high school?
If it sinks in water you know the volume and the displacement are the same.
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