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How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: wi...

Question

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [$Hint$: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (10$^3$ cm$^3$) or 62 lb per cubic foot.]

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [$Hint$: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (10$^3$ cm$^3$) or 62 lb per cubic foot.]



Answers

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [$Hint$: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (10$^3$ cm$^3$) or 62 lb per cubic foot.]

Alright. How big is a ton? Well, the tons not away measure of of bigness. It's a measure of mass, so I don't know. It depends. Depends what? You're weighing a ton of rocks. It really isn't that big. Maybe. Ah, I think it might be like three feet long, two foot wide and 1.5 feet tall, maybe, but a ton of feathers. Oh, man, that would be be gigantic. Okay, Was the volume of something that weighs a ton? Okay, I just went over that estimate the diameter of a one ton rock, so Ah, one ton rock. And I guess there saying that it's kind of like a spirit. Kal Rock. Um, I'm gonna say one ton rock is 1.5 feet. That's going to get be my guests. And that's gonna be diameter. So one time is £2000 and it says the density of a rock in, uh is three times out of water. So is three kilograms per leader. Okay. How many kilograms are in a pound? Kilograms in a pound. Okay, that would be 0.454 kilograms in a pound. He said give me kilograms um Now there is one kilogram in 10 to the third cubic centimeters. Although we're supposed to use the re times 10 to the third. Okay, Some now my pounds air going to cancel out. My kilograms are gonna cancel out, so that's going to be in cubic centimeters. Um, volume is four birds. Hi are cute. So I need to take this volume here, and I need to change it to radius. So let me just solve this. I'm gonna multiply by three. Force on both sides first. So rips 3/4 v. You know what? I'm gonna multiplied by 3/4 Pie 3/4. There were four. Pi vi equals R to the third power. So are is going to be the cube root of three V over four pi. Where V is this. And, um, I want it to be in What a great square feet. Erase, Erase Just feet. Um, I want this to be in feet. So how many centimeters air in a foot? Well, sadly, I don't know, but there are 2.54 centimetres in an inch. I have to cube that because this is cubic centimeters. No, my centimeters air. Gonna cancel out and there are 12 inches in a foot. I got a cube. That too. Okay, so now if I use this, it's going to give me the radius in feet. So let me put that into going to use Dismas dot com or a graphing calculator. Not that needs to be a graphing calculator here, So first, Q Bert keeper keeping group. There it is, uh, three over four times pi. And now I'm gonna model pie by all these conversion things. Uh, 2000 IMEs 0.454 I'm three times 10 to the third power, divided by 2.54 to the third power and 12 for the third number. Okay, that gives me a radius. And then no. Yeah, that gives me a radius, But I want the diameter, so the diameter is two times the radius, so I'm just gonna multiply this by two. Really tells me 5.7. So I'm going to say it's about 5.5 feet. It was way off. I thought 1.5 feet in man. Okay, but it's seems they indicate in the answer. There's 2.74 feet. So how am I off by a factor of two? Um, I don't know how I could be off by a factor of two. Just £2000 of a ton. 4.454 kilograms in a pound. Just gonna double check my work here three times. 10 to the third cubic centimeters in a kilogram. And that was given to us his density. Let me see here. Yep. Three times the weight of water. Oh, wait a minute. I put my three in the wrong spot. This is gonna get making way different, though. It's one kilogram per leader. So that three should have been down here because kilograms per leader. Three kilograms per leader. All right, that is definitely a problem. I'm taking the square root of this. So maybe this will fix everything. Let's see. So I need to put my three in the denominator. There we go. All right. Two point seven. You know what? I'm gonna write it as two and three force feet. This is more reasonable now. I was thinking 1.5, but I was I was more thinking more of like a I think part of my problem was I was thinking more of like a ah rectangular prism. But this is a sphere that would have gotten me a little closer. Um, all right, I was I was still pretty far off. Thank you for watching. And by the way, I demonstrated what to Dio. When your answer doesn't match up with what's in the book, think about, does your answer make sense? And since it's already in the back of the book, it does, it didn't make sense. And then and it also noticed that it seemed too high to me because I really thought it was gonna be more like 1.5. So 5.5 was way too much. Two and three force. Ah, that's I don't think I would have thought that was

Our question says that how big is a ton? That is. What is the volume of something that weighs a ton? To be specific, estimate the diameter of a one ton rock. But first, just make a wild guess. Will it be a foot a foot across three feet across or the size of a car? Hint. Rock, Hint. Rock has mass per volume about three times that of water, which is one kilogram per leader. Tend to third centimeters cubed or 62 pounds per cubic foot. So I wrote down what we were given in this problem. We were given that the density of water, which is mass per value that's density. So I wrote density as row. So the density of water, which is rows of W, is equal to 62 pounds per cubic foot. And it says that the didn't the density of rock, which I wrote his Rosa are is three times the density of water, so three times roast of W is 186 pounds for per cubic foot. It also tells us the mass of the rock in question in the mass of the rock is one time well by definition. One ton is 2,000 pounds. The question then is what is the diameter of this rock If we assume that it's ah perfect sphere. So the diameter which I wrote his D is equal to what? In order to do this, we're going to make use of the fact that the volume of the sphere is equal to 4/3 pi R to the third 4/3 pi r Who forgot pie once, right? Well, yeah, Let's write pie first to keep it consistent with what I said in common notation. Hi R to the third. Okay, well, we can rearrange us to solve for R because we want our since really what we want is distance or the diameter, but diameter is two times the radius, so solving for the radius will be just fine. In the radius, then, is three times of volume divided by floor Kai. But the radius was cube. So this entire thing is going to be too cute group or to the 1/3. Okay, well, all we need then his volume and we can get volume using the fact that we know the density of the object in question and we know the mass of the object in question because volume is also equal to the density of the object in question. I'm sorry, the mass of the object in question, which is the rock so imps of our divided by the density of the object in question. And you can check real quick with just using dimensional analysis. So the mass is in pounds and the density is in pounds per cubic foot. The pounds is going to cancel all you're going to be left with this cubic foot and volumes is in cubic foot. So we know the dimensions workout. So let's go ahead and carry out this operation. We have 2,000 pounds. Excuse me, 2,000 pounds divided by the density, which is 186 pounds per cubic foot. And if you do that, that comes out to be a 10.8 cubic feet. Okay, so now we know the volume in question of the rock so we can solve for the distance or the diameter. Excuse me. The diameter diameter is two times are Okay, so this is going to be too. Times equals two times three multiplied by 10 0.8 cubic feet divided by for pie, and all of that is raised to the 1/3 and again, the dimensions. Check out because we have cubic feet here inside the parentheses raised to the 1/3 you're going to be left with just feet and you expect the diameter to be in feet, so it works out. If you carry out this operation, you find this is equal to 2.74 feet and in assets. In the beginning, if we thought it would be approximately one foot three foot or the size of the car will, 2.74 feet is approximately three feet, so there's your answer him box set in.

Okay. In this problem of scientific measurement, we have given that when an object floats in water, it displaces the volume of water that has a weight equal to the weight of the object that has emerged. If a ship has a weight of this is w so this is 4200 55 tons. This is here, guns, how many cubic feet of seawater will it to displace? And seawater has a density of. So this is the density of seawater that age 1.25 grams per centimeter cube. And we have given one turn is equal to £2000 exactly. So first we will calculate the density of seawater. So this would be density of sea water in pounds per cubic feet. So this would be here given a 0.1 point 025 this is grams per centimeter cube. And now we have to convert this into pounds and cubic feet. So first we have to convert grams into pounds. So this will be £1 as equals to 400 and 53.59 instagram 59 g. And this is L. And now we have to convert feet into centimeters. So we have 30.48 centimeters. Makes a feet. So this is feet. And now this will be the cubic unit. So when we solve it, the city equals to £60.0 for cuba feet. So this is the density of water. And now we have to find the volume. So the volume would be in cubic feet. So this would be here the weight. So this will be 4255 tons. And we know that density is mass divided with volume. And we when we want the volume. So what long would we must divide with the density. So this is my house and didn't stay is here. This will be one divided with this is the density must divide with the density, so this would have 60 0.0. So this is here cubic feet and the £6. And now we have to convert this turn in £2. So we know that in one time there are £2000. So now when we saw that this is equal to one point 330 multiple, which 10 to the power five cubic feet. So this is the volume of the water that has been displaced.

One cc of H 20 has a massive one g one millimeter is one cc. So what is the mass in kilograms of a leader of H 201 ton or rather one metric ton of 2000 kg? How many cubic centimeters of H 20 and a ton? And if a metric count is held in a cubicle tank, what does the tank sideline? This question is testing our understanding of dimensional analysis, unit conversion. And also in the last part of the question, volumes of solids. Start off with, let's find the mass and a leader. So one leader is 10 to the third. Similar leaders. So one leader to another. Third millimeter per liter times cubic centimeter militar times gram per cubic centimetre times telegram for 10 of the third Graham is one kg per liter. HD Well. Next we want to find how many cubic centimeters are in a ton. One time time, 10 cube kilograms per tonne times 10 cube grams per kilogram times cubic centimeter H two. A program is one time some of the six cubic centimeters of HDL. Finally we have a volume of HD Well and we were told that the metric town is held inside a cubicle tank. Remember that the volume of a cube is s cube or a side length cube. So to find the take sides, we simply have equal volume equals s cubed equals 76 cubic centimeters, so we take the cube root to obtain us equals 10 and six centimeter cube or 10 square centimeters idling.


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