 In this video, I'm going to talk about the circumference and area of a circle as it pertains to geometry. So again, a couple of things that you need to know, you need to know what the circumference of a circle is, which circumference is a fancy word for the perimeter of a circle, just the distance around it. And then the area of a circle is all of the space that's inside. Alright, so these first couple of examples, what we want to do is we want to find the circumference and the area of a circle with a diameter of 3 meters. Leave your answers in terms of pi. Okay, one thing to note, leave your answers in terms of pi and then if I scoot over here to this other problem, find the circumference and area of the following figure using pi as you go to 3.14. Notice that the directions are a little bit different. This one we want to leave in answers in terms of pi. This one, we actually want to multiply times 3.14. I will show you, I did this specifically because I want to show you the difference between leaving answers in terms of pi and getting actual decimal answers for your problem, okay? So hopefully this will answer some of those questions for us. Alright, so find the circumference and the area of a circle. So what I'm going to start with is I'm going to write down the area and circumference. Actually, no. First thing I'm going to do, this problem here, it doesn't have a picture to it. This one over here has a picture, this one doesn't have a picture. So what I'm going to do is just draw myself a simple little picture. Here's my circle, here's my center, and I have a diameter, I have a diameter of 3 meters, 3 meters. And that goes from edge to edge, okay? Now, you might not need a picture for this, but it is very helpful if you want to get an accurate description of what this is. Okay, so in this case, one thing that you need to know, you need to know what the diameter is, which is 3 meters. And then you need to know what the radius is, which in this case is half the diameter, so that's going to be 1.5 meters. So I've got a diameter of 3 and a radius of 1.5. A little vocabulary there. Alright, final circumference in the area, circumference, there's a couple different ways to find it. You can either do pi times diameter, or the circumference is 2 pi times the radius. Either one of these works, it doesn't matter. Since they give us what the diameter is, I'm going to use the diameter. I'm not going to use this one, but I could use that one if I wanted to, since I actually know what the radius is. But just for simplicity's sake, I'm going to use this one. Alright, so circumference is equal to pi times the diameter. My diameter is 3, so there we are. So circumference is equal to 3 pi labels. Labels is meters. 3 pi meters. Now, notice I didn't grab a calculator and multiply it times 3.14. That's because they want me to leave my answers in terms of pi. So notice I did not multiply times 3.14. Leave the pi where it's at. Leave your answers in terms of pi. That's what that means. So my circumference is equal to 3 pi. Now, the reason that we do this is because sometimes when we're calculating circumference area, whatever it is of a circle or a sphere, whatever we're working with, sometimes the math is easier to work with if we simply just do not multiply times pi. We don't multiply times 3.14. So that's kind of the reason behind it. It just kind of depends on the problem. But in this case, we're just leaving our answers in terms of pi. Alright, now for area, area is equal to pi times the radius squared. Now for circles, we only have one formula for area. Circumference, we have two of them. You can use either one, but area, we're only going to use one of them. Alright, so pi times the radius squared. Now, we do need to know what the radius is. That's why I put the 1.5 here. So the area is equal to pi times the radius 1.5 squared. So we have to take the radius, we have to take 1.5, and we have to square it. Now, if you know what, if you kind of treat this like a 15, if you know what 15 squared is, you know that 15 squared is 225. Okay, but if I have decimals now, if I take 1.5 times 1.5, that's two decimals. So I can have two decimals in my answer. So that's actually 2.25. Okay, so 1.5 squared is 2.25. Alright, and so we're in a room here. My area is equal to, leave this in terms of pi, 2.25 pi. And my label is meters squared. Make sure you get your labels correct on this. You know the difference between a single dimension of circumference, which is just meters and two dimensions of area, meters squared. Okay, now notice that I have the 2.25. Yes, you could have decimals here. Just make sure you put them in front of pi. Don't put them behind. That's not usually how we write it. So make sure you just leave it there. If you have a repeating decimal, it's a little bit different. Sometimes you round that repeating decimal. Sometimes you don't. It just kind of depends on the problem. But this one, we didn't have to worry about it because our decimal came out nice and neat, 2.25. Okay, so on to the next one. On to the next one. Alright, let me change my color here. Alright, so find the circumference and the area of the following figure. Use pi is approximately 3.14. Alright, so now we're actually going to take our numbers and multiply times 3.14. Alright, so let's actually, let me give myself just a little bit more room here. Can I give myself more room here? Yes, I can. Smart boards are awesome. Find the circumference and the area of the following figure. Use pi is approximately 3.14. Okay, so I'm going to do the same thing except for I'm actually going to multiply times 3.14. Now, I'm also in this problem going to show you the difference between multiplying times 3.14 and multiplying times pi. There is a difference even though it's just a small difference. But here we go. Let's go on with it. Alright, so my circumference, so in this case 8 meters, it says it's right by the center. This tells me what the diameter is. The diameter is 8 meters and so my radius is 4 meters. Okay, this half of it is going to be 4 meters. Alright, so my circumference is equal to, I want to do the same thing I did last time. Circumference is pi times diameter. So I'm going to take pi times diameter. Circumference is equal to pi times, what is the diameter? Diameter is 8, I just said it. Alright, so in this case circumference is equal to, now this is where you grab the handy dandy and you take 8 times 3.14 and you get 25.12. Again, I mentioned earlier, you're going to get different answers depending on how you do this. If you multiply times 3.14, this is the answer that you get. If you multiply times 3.14, this is the answer that you get. But if you take 8 times pi, if you take 8 times pi, you're going to get a different answer of 25.13274 and more decimals after that, which this rounds to just 25.13 if you want to round to 2 decimal places. So notice 25.13 and 25.12, those are two very different answers. This one we multiply just times 3.14, this one we multiply times pi. Why the difference in the answers? Well, we have a difference in the answers because pi is a repeating decimal. It goes on and on and on and on. So what we're doing here is we're not multiplying by all those decimals as we go on. So our answers are going to be a little bit off. You have to keep this in mind if you're working with a teacher, if you're working with your classmate, whatever it is, keep this in mind. Sometimes you're going to multiply times 3.14, sometimes you multiply by pi. The answers are going to be off a little bit depending on which way you multiply. Just keep that in mind when you're doing problems like this. So if they ask you to multiply times 3.14, go ahead and use 3.14. Don't use the pi button on your calculator. That way this answer that you get is similar to what other students are going to get, but the teacher is going to get little things like that. So now that that's over, make sure that you label this. Circumference is 25.12 meters. That's a pretty big circle. Circumference is 25 and a little bit more meters. That's pretty big. All right. Now area, I'm going to go kind of quickly through this. So area is equal to pi times the radius squared. Our radius in this case is 4. Area is equal to pi times 4 squared. Area in this case is pi times 16. Now remember we're taking, we're not using pi. We're using 3.14. So if I take 16 times 3.14, that's going to be 50.24. 50.24 meters squared, meters squared for area. And there we go. That one, I went kind of a little faster. Also on the same notice last time, if I don't use, if I use pi instead of 3.14, I would get an answer of 50. It's a bad 50. Bad 5. 50.26548 with more decibels after that. And this would, if you want to do two decimal places, this would be 50.27, which is very, that's 300s off. Okay, that's actually a pretty big difference there. So this is, if we just use 3.14, this one over here is if I use pi. So again, just keep that in mind, especially with these larger numbers. You're going to get differences depending on if you use pi or if you use 3.14. Okay, so there's a couple of examples of doing circumference in area. Now, one thing to summarize to go back to, leave your answers in terms of pi. This is what the answers look like if you leave them in terms of pi. You don't actually multiply by pi or 3.14. You just leave it. Okay, you just leave it. Or some of the problems are going to ask you to multiply times 3.14, and then you're going to get decimals for your answers. Just to make sure you know the difference between multiplying by 3.14 and multiplying by the pi button in your calculator, you're going to get a little bit different answer depending on who you're doing your work with, something like that. Just keep that in mind where you're doing these problems. All right, I hope that helped you with the circumference in area of a circle. And again, just make sure you know the difference between leaving answers in terms of pi and using 3.14 or the pi button to get your answers.