>>Hi. This is Julie Harland, and I’m your Math Gal. Please visit my website at yourmathgal.com, where you could search for any of my videos organized by topic. This is Unit Conversions Part 4, we’re now going to learn how to do unit conversions involving volume, and we do the following five problems on this video. We’re going to go over unit conversions involving volume, so we’re talking something in 3D. For instance, think about this, how many cubic feet are in a cubic yard? Well, imagine that each side here of this big old cube is 1 yard, and I’ve broken it up into 3 feet because we know there are 3 feet in a yard, so actually it’s 3 feet across the bottom, and then going back it’s 3 feet, and going up it’s 3 feet. So this whole thing is called 1 cubic yard, and we could write that as yards cubed. The question is, how many little cubic feet are in there, and each cubic foot is one of these little tiny blocks, you could see it’s 1 foot by 1 foot by 1 foot, and so the question is, how many of these are in there, and there happen to be — well, if you see like this first level up in the front, you’ve got 9, and then it goes back, there’s another 9, and another 9, this is 27 cubic feet. All right. Now we know that 1 yard equals 3 feet, right? So, a simple way to figure this out is if you want to figure out what a cubic yard is, you cube both sides of this equation and you’ll have it. So that’s the same as 1 cubed, right? Yards cubed equals 3 cubed, and feet cubed, which of course we write that as 1 cubic yard equals 27 cubic feet, the same thing we got when we were looking at this box. Now we’re going to use this, since this is the same thing, a cubic yard is 27 cubic feet, remember that we’re going to start with something, let’s say that’s in 3D, so we’re going to start with something that might be in cubic feet, or cubic inches, or cubic yards, or cubic meters, whatever, and we’re going to convert it to something else that has, you know, is also going to be 3D. In other words, you can’t go from cubic feet to just inches, you have to go from like cubic feet to cubic inches, et cetera. So here’s an example. Convert 5 cubic feet to cubic inches. Basically what this is saying is if you’ve got 5 cubic feet, you’re trying to get this answer, how many cubic inches? All right. So keep in mind, that’s what we’re trying to end up with. So how could we get there? So we have 5 cubic feet, and I want to end up with cubic inches, and so you have to think, is there a relationship between inches and feet that you already know. And we’re going to multiply by the fraction that would equal 1, so that would be — well, we know there’s 12 inches in a foot, so I could multiply this by — I know there are 12 inches in 1 foot, correct? But of course, you see how the — I have a foot cubed in the numerator, and I only have a foot in the denominator, so I need a cubic foot. So here’s the trick, we’re going to cube this fraction. Remember this fraction equals 1, ’cause 12 inches is the same thing as 1 foot. So, we’re going to cube everything in the numerator and denominator, and that way we will be able to cancel out the cubic feet. So, in the denominator, notice I’ll just have a 1 cubed, which is 1, so I’m not going to end up with a fraction in this problem. And I’ve got 5 times 12 cubed inches cubed, so that you could do on your calculator, you could do 5 times 12 cubed in your calculator. Remember you need to do the 12 cubed first, and then multiply by 5, unless your calculator does order of operations, and you’re going to have inches cubed, and whatever that is, that’s what goes up here on this blank. And hopefully you put that into your calculator, and the answer is 8,640 cubic inches, it’s a huge difference, because think about how if you had, like, like a box, 5 feet by 5 feet by 5 feet, think about how many little tiny, you know, cubes that are just 1 inch by 1 inch by 1 inch that would fit in there, so that’s one way of thinking about that. Okay. Here’s the next one. We want to fill in the blank, we’re going to use the approximation that 1 inch is about 2.54 centimeters, so then you’ll have an equal sign here, I guess to be a little bit more accurate, I’ll say, oh, it’s about how many cubic centimeters. All right. So put the video on pause and see if you can figure this out on your own first. All right. Let’s try it. So we’ve got 7 cubic inches, and I have to think, what do I know about the relationship between inches and centimeters, and I’m going to use this approximation, 1 inch is 2.54 centimeters, and I want the inches to cancel out. So I need the inches in the denominator. So I’m going to put 1 inch, I know that’s the same thing as 2.54 centimeters approximately, and of course that’s not going to cancel out the inches cubed, ’cause I only have 1 inch, but if I cube everything, I’ll have it. Now of course I don’t have to write 1 cubed if you realize 1 cube’s always going to be 1, that’s up to you. The inches cubed now will cancel. And so on your calculator, we could do 7 times 2.54 cubed, and I’ll have my answer that I want, so it will be cubic centimeters, so you want to get out your calculator and try that. Now when I put that in my calculator, I got 114.709448, and I know there’s some rounding going on here, so I’m going to have to round this to something, so let’s just say that we want to round to the nearest cubic centimeter, okay? So we’re going to round to the nearest cubic centimeter, that will just be 115 cubic centimeters. If I was doing it to the nearest tenth, it would be 114.7. All right. Here’s another one for you to try. We want to fill in the blank, so what we’re doing is we’re going to convert 82 cubic feet to cubic yards, and we want to round to the nearest tenth of a cubic yard. So put the video on pause and try this on your own first. All right. So let’s see. We start out with 82 cubic feet, and I want to end up cubic yards, so the first thing is, is their relationship just between yards and feet, and I know in 1 yard there is 3 feet, and of course I wanted to put it, the yard in the numerator and the feet in the denominator ’cause I’m trying to get that, the feet to cancel out. And now we need to cube everything so we have actually cubic feet to cancel out. So notice this is the first time we’ve gotten something in the denominator, I’ve got that 3 cubed, which is 27, but the cubic feet cancels out so I say my answer’s going to be in cubic yards. So on your calculator, you’re going to end up with 82 in the numerator, right? Over 27, and that will give my answer, and so what we want to do is just put that in the calculator and round to the nearest cubic yard, so we just do 82 divided by 27, and I have 3.037, so if I’m going to round that to the nearest tenth of a cubic yard to show that I’m really going to the nearest tenth, I’m going to write that as 3.0, it means I did pay attention to the hundredth place. If I were going to round this to the nearest hundredth… [ Background noise ]>>Of a cubic yard, the answer would be 3.04 cubic yard. If I were doing it to just the nearest cubic yard, I would just write 3. It’s a little bit tricky, ’cause 3.0 is the same thing as 3, but I’m only writing is as 3.0 to show, show you that I was actually rounding to the nearest tenth. All right. Here’s another one. We’re going to fill in the blank using the approximation 1 inch equals 2.54 centimeters, and in the end, let’s round this to the nearest cubic centimeter, all right? So we’ve got 2 cubic feet and we’re trying to go to centimeters cubed, and I don’t have a direct computation between feet, cubic feet and cubic centimeters, but I do know I can go from feet to inches, and inches to centimeters, so that’s the trick here. So let’s start off with 2 cubic feet, and first let’s change that to cubic inches. So how do I do that? Well, I have to think of the relationship between feet and inches, and I want the feet to cancel, so I’m going to put 1 foot is 12 inches, and of course I need it to have cubic feet, so I need to cube everything. I’m not, I’m not — well, I’ll go ahead and write the 1 cubed. All right. Now see how the feet cubed are going to cancel? But I also need to get from cubic inches to cubic centimeters, so I have to do something else here. I know the cubic feet are going to be able to cancel, but I’ll have my answer in cubic inches. So now I’ve got to use the conversion between inches and centimeters, which I have up here, 1 inch is about 2.54 centimeters. So 1 inch is about 2.54 centimeters. And I want to cube everything here as well so that I can cancel out the cubic inches. ‘Kay? So finally, what am, what am I left with? Well, I’ve got the 2, right? Then I have a 12 cubed, and then I’m multiplying that by — I’m going to use parentheses, it might be easier. I don’t want you to get confused with the dots, put the decimal point. Cubed, and then my answer’s going to be in cubic centimeters. So now, we put all that in the calculator, see what we get and then round to the nearest cubic centimeter. All right. When I plug mine in the calculator, I get 7200, and then I have 4.7, so that would be rounded to the nearest cubic centimeter, 72,005 cubic centimeters. All right. So, that’s how we can do some conversions within volume, now if you’re going from metric to metric, let’s just do one problem like that. All right. Let’s say we want to convert 3 cubic centimeters to cubic millimeters. In other words, I start off with 3 cubic centimeters, and I want to end up with cubic millimeters. All right. So we have to know the conversion between centimeters and millimeters, and there are 10 millimeters in 1 centimeter, so you do have to know the metric system, or be able to look that up. So, I’m going to multiply this by — I know that there are 10 millimeters in 1 centimeter, but I need to cancel out cubic centimeters, so I’ve got to cube everything so that the cubic centimeters cancels. We’ll have just a 1 in the denominator, so all I have to do is multiply 3 times 10 cubed. I don’t think we need a calculator for that, 10 cubed is 1,000, right? It’s a 1 with three 0s, and 1,000 times 3 is 3,000, so the answer here is 3,000 cubic millimeters. All right. So just keep practicing. [ Silence ]>>Please visit my website at yourmathgal.com where you can view all of my videos which are organized by topic.