 Thank you. Yes, like I said, welcome to the basic numeracy online session and remember to complete the register. If you have any questions relating to the technical, the system, UNISA processes, please send an email to CTNTAT at unisa.ac.za. Okay, if you have content related questions where you're struggling with either your BNU module or your QMI module, you can send an email to me, eboy, eboyem at unisa.ac.za. And I should be able to respond or set up a session or respond to your email as well. Welcome. Today is the 15th of August. My name is Elizabeth Boy. I will be your facilitator for the rest of the semester this year. We are not going to start from the beginning because the semester is too short. The first semester we had dealt with some of the content, almost 80% of the content that BNU and QMI requires to give them some sort of an idea or a guidance in terms of how to write or complete your assignments. Or also give you some type of a guidance or assistance in writing your exam. So we covered a lot of content today and because we didn't cover all of the content, so I decided for the second semester we're just going to make sure that we cover most of the content that was not covered in the first semester. I asked Unisa to also share the recordings of the first semester recording so that then you can go and watch them at your own pace. If they don't update them, but I can show, I will show you where the backup copies are and you can go and watch the recordings anytime you want for the majority of the content. What we have covered in the first semester, it is also available online. The way you signed in to the schedule, there is a link that says notes and recordings. If you go to that link, you will be able to access the notes for today and also for first semester. And that will also help you when you're watching the videos, you can follow through the notes. I always use presentations and slides because it's easy, readily available information there. I just write when I need to do some activities. So you will have all the notes on there as well. Okay, so for those of you who it's their first time attending basic numeracy, I just want to orientate you so that you along the way, when we are busy with the sessions, there are no confusions as well because these are skills numeracy training workshops that are not module tutorials and related sessions. So yeah, we deal with skills, how we help you unpack the content in a way that it makes it easier for you to understand and also for you to be able to do your assignment and also to go and write the exam. So with numeracies, it involves being able to think, communicate quantitatively with the information provided to you. We help you to make sense of the information that you have in front of you. And at some point we want to also make sure that you are aware in terms of the spatial awareness, right? And you also understand the patterns and sequences and also recognize some of the solutions where mathematical reasoning can be applied to solve problems. But not only that, we also try to fit it in a way that it also aligns to your module, whether you're doing BNU or you're doing QMI. So I'll give you some tricks and terms and things to help you understand your module better, right? And we're going to follow a structured program where you can look at where you find the notes. There are also two Excel spreadsheets which are our session plans. It gives you guidance in terms of the type of topics that we will be covering for this semester as well. So these are some of the topics that in general in numeracy we would have covered. Some of them we already covered in semester one. Some of them we're going to cover in this semester. So you will see that today we covered in measurement. Next week I think we covered in ratios and percentages. And these are things that we, and proportions and ratios. These are the things that we didn't cover last semester. So we're going to make sure that you also have some sort of information relating to those ones. Okay, so in terms of the numeracy focus, I'm not going to go into details of this. The process that we go through is to identify the skills gap that exists within students who are doing these two modules. And we did this in previous years because I used to be a tutor. I would look at how, and I was a face-to-face tutor. So it made it easier because I was able to see when I'm explaining some of the concepts in the classroom. I would identify where the students are struggling with and the type of things that they are struggling with. Like for example, how do they do some calculations? How do they use their calculator to make calculations? All those things. So we ended up identifying those skills gap and formulating. Then they become part of the academic or the numeracy facilitation sessions, where we concentrate mostly on making sure that we close those gaps as well. And you will see that most of the time we will use just generic information and we will try to bring it back to your life experience as much as possible if it's possible. And we will also try by all means to visualize it because sometimes it's easy. Some people learn in different ways. Some learn by looking at the diagram and it makes sense to them. Some learn by just looking at the numbers and they can understand what is happening. So we are going to try and make sure that we accommodate everyone as well. So in terms of the process that I normally follow when we do these sessions together, I use the problem solving approach, which is a Newman's prompt approach. This method or this skill, it helps you as a student or as a person to understand what the problem is and how you're going to solve it. So it gives you also some of those steps because if you know the steps on how to solve that problem, then it will make it easier to answer the question that will be given to you. So normally what I encourage you to do is the first time you see a question, read it and read it again, but now when you read it for the second time, try to read it and understand it in your own ways, interpret it in the way you understand it, not in the written English that they have it, but in the rephrase it the way you want to understand what the question is asking you to do. Once you do that, then the next step, you're going to ask yourself, if I know this is the type of a question that I am given, what are they asking me actually to do? Are they asking you to simplify? Are they asking you to describe? Are they asking you to solve something? Or are they asking you to multiply, to divide? What is it that they are asking you? Because all this process of doing all these mappings will help you identify the things that you need because then the minute after you know what the question is asking you to do, then you're going to find ways of how you're going to answer the question because then you're going to use different things because when you were asking yourself what is this question asking you to do, in the same time you will be identifying the important facts and that is very important. Identifying the important facts are if they give you the length, you must write it and say they gave me length equals and the number that the length is. If they gave you the width, the width equals and you write it down then once you have all the important facts that you have looked from the problem that they were giving you, you can also use a diagram to draw that because if you look at the things that they gave you they might say this is a rectangular shape. You can draw a rectangular shape and they will say it has a length of, you can also put the length, they have the width of this much, you put the width, you create this, you visualize it in a way that it would make sense for you to further answer the question that they have asked you to do. So once you have all the important facts you have drawn, you've needed all the help, now you know what you need to do. You also need to make sure that you identify the either, the equation that you need to be using. So for example, if it's an equation or if it's a formula, what kind of a formula did you need to use in order for you to answer this question? You write out that formula and then once all that steps are done, then you go and do your calculations. You will either do your calculation using your calculator or calculations doing it manually. What I don't expect you to do is read the question, take your calculator and start calculating. That will not help you to understand the process. So we want you to be able to know that you need to do certain steps before you can pick up your calculator and start doing your calculations. Once you have done all your calculations, right, once you have calculated everything, I want you to go back and reflect on your answer. Sometimes in a section like this we're going to do what we call a feedback loop, where we're going to have an exercise where you do your exercise, you have your answer and then we're going to come back and do it together so that we can see and also help others in order for us to be aligned and make sure that we also are validating the answer that we got. And that is the process that you always need to do. Always the minute you got the answer, try and go back and reevaluate that answer to make sure and double check that it is the correct answer. And that is the process that we're going to follow. I know that it took long, but I needed to also explain this because that will be the process that most of the weeks we're going to follow that until the end of the sessions. We will be using this approach. So I know that it might still be fresh in your mind, but you will hear me constantly when we're doing some activities asking you what do you understand that the question is asking you. What are the things that they are giving? What type of equation or formula do we need to use? Then I will say let's do the calculation and then we start doing the calculation. And then I say let's check our answer. Did we do it right or wrong? And those will be the steps that we go into follow. So I'm not going to say it explicitly to say let's use problem solving approach. I will just base it in our conversation so that you get used to and doing this as well. Okay, so that is the end of the introduction. Are there any questions or comments before we start with this session today? Are there any questions, comments? Nothing on my side. Thank you. No worries. Then let's get to it. So today we're going to be looking at measurements. The only tool unit is the calculator. Other than that, you also need to remember the formulas that we're going to share with you and the SI units. You will need to be able to practice that. Okay, so by the end of the session today, you should be able to learn how to convert length of unit, determine the perimeter of different figures, the area of different figures, volume of different figures and also convert from liters to cubic units. So when we convert length from one unit to the other, we always use the SI units, which is the system of instrument unit that we use to convert from one unit to the other. And always the length we always assume or use meters. It's always assumed that for a length, we will always refer to meters, right? So in order for us to move from one unit to the other, there are certain rules that you need to remember. Now, this is your SI unit. They start from millimeters to hectometers or kilometers to millimeters, actually. It starts from kilometers to millimeters. What you need to know is if you're moving from a bigger value to a smaller value, if you're going to convert from a bigger value to a smaller value, you need to multiply by 10. If you move from a smaller value and converting to a greater value, you will have to divide that unit by 10. So you always divide by 10 when it comes to meters or millimeters or centimeters, kilometers, when you move it. So for example, if I want to move from 20 centimeters to 20 millimeters, so where is my 20 centimeters? My 20 centimeters, so moving from a centimeter to a millimeter, it means I'm moving from a bigger to a smaller. So it means I need to multiply by the appropriate value. Alternatively, you can use another mathematical function to change from 20 centimeters to 20 meters. What do we know? We know that 10 millimeters is equals to 1 centimeter, and we want to move to millimeters. So I want to move to my X millimeter. My X is my unknown, my number, which is my placeholder for the unit that I want to move to, and I'm converting from 20 centimeters. And now in meds, to simplify this, because if I know that 1 centimeter is equivalent to 10 centimeters, because I need to multiply by 10, I multiplied 1 millimeter by 10 to get 10 millimeter. And to simplify this, I need to cross. So it means my X millimeter will multiply with my 1 centimeter, my 20 millimeter will multiply with my 10 millimeters. So I'm going to write it right here at the bottom. I'm going to say my 10 millimeters multiplied by my 20 centimeters equals my 1 centimeter multiplied by my X centimeters. So from here, I want to send not centimeters, but millimeters. I want to be left with only the millimeters. So I'm going to divide the side by 1 centimeter, divide the side by 1 centimeter. 1 centimeter and 1 centimeter will cancel out, and then I will be left with my X millimeters. I'm just going to write X and this side I am going to cancel my centimeter with my centimeter, and I will be left with 20 times 10, 200 millimeters. So it means when my X millimeters that I didn't know what those are, I will be able to find it and say that is equals to 200 millimeters. If I don't apply this, I must always remember that to move from a meter to millimeter, I must multiply by 10. So I have 20 centimeter and I need to move to millimeter. So I'm going to take my 20 and multiply by 10 in order for it to give me my 200 millimeters. Because I need to multiply that 200 centimeter by 10 to convert it. And that's what the rule says. If you're moving from a bigger veil to a smaller veil, you need to convert by multiplying with an appropriate 10. Your exercise is to answer number one. We have 250 kilometers to meters. We're moving from a bigger number or a bigger unit to a smaller unit or I can stop right there to a smaller unit. So if I'm moving to a smaller unit there, how many 10s will I have? One, two, three, 10s. Are we winning? What do we know? We know that there are 10 times 10 times 10. There will be a thousand. So there will be from kilometers, 10 times 10 is a thousand. So there will be 1000 millimeters in one kilometers. Sorry, not millimeters, but meters. So if we know that we have X meters that makes up 250 kilometers, therefore we're going to crisscross our X will multiply with one K and 1000 meter will multiply with 250 kilometers. And we're going to divide that by one kilometer, one kilometer. And therefore X one kilometer will cancel with the kilometers. Then we have 1000 times 250 kilometers, which will be equals to 250,000 kilometers. Happy? Let's look at number two. Number two it says we need to convert from a smaller to a bigger. Now, since we're moving from small to bigger, we will have to divide by 10s. How many? We know that there are 10 millimeters, which are equivalent to one centimeter. And here we have 1300 millimeters and we need our X, which will be our centimeters. So crisscrossing X will multiply with the 10, we will have X. And one centimeter will multiply with 1300 millimeters, and we're going to divide by 10 millimeters. Millimeters and millimeters will cancel. What else? A 10 and a 10 will cancel. So it will be one times 130 will be equals to X is equals to 130 centimeter because we are left with only 160 meters. And that's how you convert from one unit to the other on your own. At your own time, you can do exercise number three, four and five. The same concept will apply if we're moving from big to small, we divide if we're moving from small to big, we multiply. A centimeter to millimeter, it is small to big, a millimeter or a meter to millimeter, it is big to small. So you need to remember all that, that when you're moving from one bigger unit to a smaller unit, you divide when you multiply, when you're moving from a smaller unit to a bigger unit, you divide by the relevant 10s. Are there any questions? If there are no questions, then we can move to how do we calculate the perimeter of an object? A perimeter, in a way, it is the distance around the figure or the object. If you are in a house, the perimeter of a house will be the walls outside, you just measuring the walls outside the house. That is the perimeter. And we can calculate the perimeter of a rectangle and the perimeter of a rectangle, like I said, because we're just adding up, the perimeter of a rectangle will be adding all the sides of the rectangle. The rectangle has the length and the width, length and the width. So it will be length plus width plus length plus width, which is the same as two times length plus width to calculate the perimeter of a square. A square has four lengths or four sides that are equal and they are denoted by length. We can calculate the length plus the length plus the length plus the length, which is the same as four times the length. The perimeter of a triangle, it's easy because we just add all the sides. If this has the side PQR, then we just add the side PQR. The only object that when calculate the perimeter is not as straightforward as adding all the sides, because it does not have the sides, it is round in its nature. It's the circle. To calculate the perimeter of a circle, we use the formula 2 pi R, where our pi, you're going to use their function on your calculator. If you don't know the function on your calculator, you must go and look for it. If you are using a casual calculator, your pi will be at the bottom next to the common or the decimal next to the answer. There is a button with x times 10 to the power. It's got a pi function. Pi function next to it. It's written in orange. You will have to press the shift first and then press the pi button. If you are using a casual calculator, you just need to look for the same pi function. If it's written in orange, for casual, you press shift for sharp. Whether it's sharp financial calculator or sharp scientific calculator, you will press second function and you will press the pi button. Just look for that pi button. Do not use the 2 divided by 7. Use the actual pi function when you are calculating. Your R is your radius. Your radius is the distance between the outside of the other side of the circle to the other side. So from this side to that side, we have what we call a diameter. And a diameter, when it is split into two equal parts, it creates what we call a midpoint. And that midpoint creates two equal parts of which one of them we call it the radius. So you will need to remember that for a circle, we use 2 pi R. Your pi is the function on your calculator. Your R is your radius, which is half of your diameter. So let's look at how we calculate the perimeter. So since the rectangle has four sides, two opposite equal sides, so we use the formula. C is equals to 2 times L plus W. And if we need to calculate the perimeter of a rectangle with the length of 80, so we're going to state what we are given, the length of 80 meters, and the width of 8 meters. The width of 8 meters, so there we've got what we are given. And the question is, we need to calculate the perimeter and we know what the formula is. And we can then just substitute because we already identified all the facts that we need to answer the question. So substituting into the formula, we know that formula is C is equals to 2. And the perimeter is always referred to with the C and a C in a way it's also called a circumference. A circumference and the perimeter, one and the same thing when it comes to measurements. So C is equals to 2 times L plus W. Our N is 80, our W is 8, so 80 plus 8. The other thing that I need to pay attention to is to always remember in maths, we use what we call the Bodmer's Rule. If you don't want to apply the Bodmer's Rule and you want to use your calculator and do everything on your calculator, always remember to use your brackets. It is very, very important that you also include your brackets. Do not say 2 times 80 plus 8. It's not going to give you the right answer because the Bodmer's Rule says brackets first, then addition and subtraction comes later, division and multiplication before addition and subtraction. So please remember that you need to apply the Bodmer's Rule. Or if you are using your calculator, always to include the brackets. So 80 plus 8 is the E8, the E8 multiplied by 2 is 76 and the perimeter of this rectangle is equals to 76 meters. Sometimes in your modules, they might give you the units in meters and then they expect you, in your options, they give you the answer in another unit. Therefore, they expect you to know how to convert from one unit to the other, like we did just now, converting from one unit to the other unit. So you must pay attention to the options as well. This is your exercise. And on this one, I'm not going to do it for you. You are going to give me the answer. Can't play the circumference of the following figure. Remember, circumference, perimeter, one and the same thing. An area with the length, or sorry, a rectangle with the length of 15 centimeter and the width of 8 centimeter. You want the circumference of this figure. Let me know when you are done. Yes. Okay. And that is correct. Correct. Yes. Anyone who wants to explain it so that then I'm not the only one. So we are told that our length is 15 centimeter. Our width is 8 centimeter. And we know what the formula is. C is equals to 2 times the length plus the width or breadth, length plus breadth or length plus width. It will still mean one and the same. And 2 times our length of 15 plus our width of 8 and 2 times 23, which is equals to 46 centimeters. That's how you will answer the question. Easy, right? Same for the square. It has four equal sites. And if we need to calculate the perimeter of the square with the length of 80, which is what the formula is. So we know that this length and that length and this length and this length are the same. They are 80 centimeters. The formula is C is equals to 4 times L. So since we are asked to calculate the perimeter and the perimeter is ailing all the sites, we can then substitute into our formula and calculate. 4L is the same as 4 times 80. And that gives us the perimeter of 320 centimeters. Easy, right? I'm tempted to say also do this exercise. It would be quick and easy. Calculate the perimeter of a square with 27 centimeters. A square has four sites, right? A square has four sites. So let's look at the formula. Even if you don't look at the formula, because we are ailing the sites, it's easy. 27 plus 27 plus 27 plus 27 plus 27. So you will add 427. Yes, that's correct. So we know that this length is 27. This is 27. This is 27. This is 27. The formula is C is equals to 4 times L. And therefore it will be 4 times 27, which is equals to 108. So it's written chess. I got a little confused with 4. So I put the 2 instead of 4 and then I got a draw. But thank you for correcting me. No worries, no worries. So for a triangle, it has three sides. So we just use, we add all the sides. P plus Q plus R will give us the perimeter. Calculate the perimeter of a triangle with the sides. 10 centimeters, seven centimeters and six centimeters. Just making assumptions. If this is 10 centimeters, 10 centimeters, 7 centimeters, 10 centimeters, I just add all of them. So perimeter, meaning adding all the sides. The formula for a triangle is A plus B plus C or P plus Q plus R, depending on the sides that are labeled. So our C will be 10 plus 7 plus 6, which gives us 23 centimeters. Calculate the circumference of the following figure of this triangle with the sides 33 centimeters, 27 centimeters and 25 centimeters. The other easy one. It's easy when they give you normal figures like this. 85 centimeters. Yes. We know that it's the C is equal to, since I don't have letters on this, I can just add the values plus 25, plus 27, which gives me 85 centimeters. And that is the circumference of a triangle. For a second, a second has a diameter and in the middle of that diameter it's what we call the midpoint distance between a midpoint and the diameter. It's called a radius. Whether I move from here to there, that will still be my radius from here to here. That will still be my radius from here to here. That is my radius from here to there, radius. As long as it's from the midpoint to the side of the cycle, it is there referred to as the radius. And a diameter is made up of two radiuses. To calculate the circumference of a cycle, we use two pi r. Example, calculate the circumference of a cycle with a radius of four centimeters. Oh, sorry, of four meters. Here they gave us the radius. So it makes it easy to substitute. In the exam or in the assignment, they might not give you the radius, but they might give you a diameter. Always remember that if they gave you a diameter, you just need to make sure that you divide that diameter by two so that you create a radius. So we are told what the radius is. We just come and substitute into our formula. C is equals to two pi r. C is equals to two times pi times four. Remember to use the function from your calculator. If you are using, if you are using a ratio, remember it is shift and the button way, it is written EXP or 10 to the power of X, something exponent. There is a pi function there. You must use that. So that will be two times shift pi times four equals. I do get 25.13. Your question, calculate the circumference of this figure with the radius of eight millimeters. So we know that the circumference is two pi r. And we are told what the r is. R is two pi times eight. And the answer, I don't know what kind of calculators you have. If you're not struggling with your calculators. See, do you have an answer? Yes, I get also 26. I'm sorry, 50.27. And the answer will be 50.27. Millimeters. It's easy when you have normal shapes. When you have what we call irregular shapes. So there we had regular shapes, right? Like your triangle, rectangle, cycle, and a square. Those we call them regular shape. When you have irregular shape and they ask you to calculate parameter. Still the same concept applies because the parameter is adding all the outside. You just add this side plus that side plus this side plus that side. The same on this shape. You're going to add all this side. Even if it's on a five, it's got five sides. You just going to add all the five sides. A parameter means adding all the sides. So calculate the perimeter of an irregular shape with five sides of 14 centimeter, 9 centimeter, 11 centimeter, 18 centimeter, and 7 centimeter. So because it's five sides, I can use this. If this one is 14 centimeter, doesn't have to be like this much. 14 centimeter, 9 centimeter, 11 centimeter, 13 centimeter, and 7 centimeter. With the parameter, I just add all the sides. So it's 14 plus 9 plus 11 plus 13 plus 7, which will give me 54 centimeters. That makes it easier when you have an irregular shape. So now I'm not going to ask you to answer this because it's the same exercise like that. So let's look at when you have a composite site. A composite site is a figure or a composite figure. It's a figure that has two in one or multiple figures that you can see from the graph. Because if I cut this either here at that point, I will be creating two rectangles. If I cut this figure at this point, I might be creating a square. But I'm not sure if this is a square. But I mean, it might be two different figures. So those we call them composite figures. So to calculate the perimeter of a composite figure, it's also still the same applies because it's adding up all the sides. Now the challenge comes when some of the signs are not labeled or do not have values. So from this point to that point, which is this figure, which I can call it X, there is no amount. So we don't know what is the distance between that and that. Also from this point to that point, I can call it Y, there is no number. However, we are given some other side. We are given from this side to that side. From this point to this point, we are told that it is 25 cm. And we are also told that from here to there, it's 8 cm. If I extend this, the distance between that point from here to here should be the same as the distance between that point to that point. So it means the distance will be 25. Then it means I should be able to find this missing part Y. So this missing part Y, I can calculate it by adding Y plus 8 should be equals to 25, right? Y plus 8 should be equals to 25. Or Y should be 25 minus 8, because I know what 8 is. Say the distance from here to there, we don't know it's X, but the distance from this point to that point there is 30 cm. So it means if I know the distance from this point to that point and it's 4 cm, I can find my X and my X will be the same as 30 minus 4, because I know the length of this piece. It's 4 cm. So in order for me to add the sides, I know that I'm adding by 30 plus 25 plus 8 plus 4. And I'm going to add my X, which is 30 minus 4. See there. And I'm going to add my Y, which is 25 minus 8. And that gives me the composite figure has the perimeter of 110 cm. Is it right? Yes. Sorry to interrupt, ma'am. I just wanted to ask you. So we're busy with perimeter right now. And perimeter, I'm just wanting clarification on this. Does that mean that we always add, and if we do the area, we multiply? Yeah. So I'm going to get to the area just now. So the perimeter, we add the outside. Okay, thank you. So in the exam, I just used a simple question, right? To help you answer the simple figures. In the exam, you don't get simple figures. You get figures like this. But if you understand the concept of a perimeter, then it should be easy for you to answer this question. The other option here is this is a half a second. It's not a full second. We know that a second circumference is 2 pi r. Since it's half, we're going to divide it by 2 to split it into 2. And therefore, the circumference of this will just be pi r. So in order for us to add the circumference of this whole picture that we have, and they say we need to calculate the circumference of the following figure. Then we go into calculate the circumference by adding this piece that we have, which is pi r plus 6 centimeters, right? Let me remove the centimeters. We will deal with them when we are done. Six plus, we also need this length, which is 4.8 plus. We also need to remember this. It is 2 centimeters. So I don't want the centimeters plus the 6 centimeters. That's again another 6 centimeters. So now, how do I find the radius of this? They told me in terms of this line, the dotted line, it says from this distance to that distance, it is 4 centimeters. So therefore, it means from there to there, it will be 4 centimeters. So my radius is 4. So you just say pi times 4 plus 6 plus 4.8 plus 2 plus 6. And that will give you the circumference of this figure. And that will be equals to 31.37. 31.37 centimeters. That is the circumference of this figure. So let's see in the next 20 minutes if we can cover the rest of the other session. We're not going to spend more time on the next one. So we're going to be able to calculate the area of different regular shapes as well, like the rectangle, the square, the triangle, and the pi. And always remember that the area because we are multiplying, the unit will be squared because it's multiplying the units by 2. So you multiply the units twice by itself. So it will be squared. So the area of a rectangle, it will be length times width. And if we need to find the area of a rectangle with the length of 30 and the width of 8, we know that our length is 30, the width is 8. The formula is A is equals to L times W. You substitute the values into the formula and you will find the area will be equals to 30 meters times 8 meters, which is equivalent to 240 meters squared because it is meters times meters. So the area of a square is given by L squared because there are sides. So one thing you need to remember, the perimeter we said is the outside. The area, we're talking about the shaded part, all this red part. Right? That is the area. So we calculate from this end to that end, this end to that end. I never knew that. I never even knew that. If you have been in a house and you bought tiles, you will always remember when you go buy tiles, how many square meters, because they are counting the area of the room. So we use the flat side from wall to wall. So for a square, we use L times L, which is L squared. So if the length is 80 centimeters, it will be 80 times 80, which is 64,000 meters squared. For a triangle, it's different. Your triangle has to have a right angle in order for you to have this height. So they will give you a triangle with a 90 degree line, which creates a 90 degree line, a perpendicular line to where the base is. So if they create a 90 degree here, then it means Q is your base. If they create it here, then it means P is your base. So you need to pay attention to the 90 degree angle. So your 90 degree angle is parallel to your base. Oh, sorry, it's perpendicular to your base. So your height will be the line that creates a 90 degree perpendicular line to your base. And the area of a triangle is calculated by using half times base times height. So if we have a triangle with the base of seven and the height of six, we just substitute into that formula. So if our height is six and our base is seven, you just come to the formula and substitutes. Half times seven times six will give you 21 centimeters squared. And that is a triangle. For a circle, we use pi r squared. So this is for a full circle. We use pi r squared. Remember, r is your radius. D is your diameter. And pi is the function on your calculator. If we need to calculate the area of a circle with the radius of 14 meters, then we just substitute our 14 into r. And we get the area of a circle to be 615.75 meters squared. I'm not going to worry about number A. We're going to do number B. B says calculate the area of the shaded part. Now, this is a composite figure. Why am I saying it's a composite figure? Because they've got a circle and the white area is a rectangle. Because the side of one side of a rectangle is 3 centimeters and the other side is 4 centimeters. So it has two opposite equal sides. And they also gave us the diameter, but not the radius. Because now I'm trying to figure out what am I giving, what are my effects here? So the point from here to the other side, it's got a midpoint of 5 centimeters. So therefore, this is my diameter. So it means in order for me to find my radius, I'm going to say D divided by 2, which is 5 divided by 2, which will be 2.5. So my radius will be equal to 2.5. And that is not the end. They say I need to calculate this shaded area. And this shaded area, so area of the shaded part, is given by the circle, area of a circle, minus the area of my length times my breadth. Because I need to take away this box. In order for me to find only the shaded area, I need to remove the box. And removing the box is your rectangle. So then my pi times my radius of 2.5 squared minus times my length of 4 times my breadth or width of 3. And this will be equals to 2.5 squared times pi. It's equals to 19.63. And I'm going to subtract. They equal first 2.5 squared times pi equals 19.63, minus into bracket 12. Actually, I should have just said 12, because 4 times 3 is 12 minus 12. And the answer we get is 7.63. Sentimeter squared. You must also remember the unit, which are centimeter, centimeters. If in the exam sometime they give you two units that are different, please convert one to the other so that you wake him with the same unit. The last section that we need to look at is the volume. So in order for us to calculate the volume, the volume is how much can we fit into a cube or a cylinder or a can? You know that in a can, how much can we fit? How much drink can we fit into that can? That is the volume. It measures the capacity of the three-dimensional object. So I'm going to look at three of them. The cube, prism, and a cylinder. A cube is a square, a prism, rectangle, and a cylinder is for a circle. Now we're going to use the area and also the height, because if you look at the square, let's take the one at the top. If you look at the square, this square is extended by the height. And it has another square at the bottom, but because we're only interested in the volume, we're going to calculate the area of this, multiply it with the height. The same rectangle is elevated by a height. Same circle is elevated by the height. We're going to use the area, multiply the area with the height. That's the formula. If you forget how to calculate the volume, just always remember only those things. So the volume of a cube will be your L times L times L, which is L times L is L squared times L, which is the height, makes the volume to be L cubed. Now with a prism, then it's length times breadth, remember that is the area of a rectangle, times the height of that rectangle. For a cylinder, you're going to use your area of a circle, times the height. So you can see that it's pi r squared times h, and those are the formulas that we're going to be using. So let's look at, before we look at how we calculate this. When it comes to volume, sometimes they will give you the figures in meters and millimeters and centimeters, and then you need to convert it to liters. And that's why you need to know and remember the conversion table. It is very, very important. You need to always constantly remember that one liter is equivalent to 1,000 centimeter cubed, and it is equivalent to 1,000 milliliters. So one liter is equivalent to 1,000 centimeters, is equivalent to 1,000 milliliters. So therefore it means centimeter cubed is equivalent to millimeter. I don't understand anything you say. I'm not good. So you need to always remember that a liter is made up of 1,000 centimeter cubed, and a milliliter is the same as your centimeter cubed. Otherwise you can also apply any of the units changes because you need to be able to convert, if they give it to you in meters, you need to be able to convert it to liters because we're talking about volume. It's always measured in liters and milliliters. Okay, so let's look at these questions. We'll see how far we get because this is the end of the session. A circular water reservoir has a maximum capacity of 10,000 kiloliters and its diameter is 30 meters. Now if you look at the two things, not in the same units, right? So it means we need to do some conversion. So we have kiloliters and we have meters. So going back to the table, we need to look for kiloliters and meters. On this one it didn't even give me the kiloliters and meters. Kililiters and meters. So we will have to convert our meters into liters. Let's see, one meter, 1,000 meters is equivalent to one kilometer. But that is not equivalent to... Let me just double check something. Overlook, right? One is there, I think, called kiloliter. Is that not show? No, it's not there. I don't know this, don't worry, you're not alone. Okay. Because we need to convert meters to liters. So the only thing that weighs me off is this kiloliter. What is a kiloliter? Can I assume that in terms of kiloliter will be equivalent to... What's kilo? Kilometer. So kiloliter. Kiloliter. Kilometer. Kilometer is KM cubed. And then what is kiloliter? Let's Google that. I'm going to waste more time with that. There is Google. Kiloliter. Let's convert kiloliter to meter. Kiloliter to meter. Because it will be easier if I work with a meter cube to meter cubed or centimeter cubed. So kiloliter, one kiloliter is equivalent to one cubic meter. One cubic meter, right? That's what I get. So it's the same as milliliters. So no, one kiloliter is equivalent to one cubic meter. She's centimeter cubed, right? Yeah, it's the same as milliliters on the conversion chart you showed us before this page. So let's go there. So we set one cubic meter is equivalent to one milliliter. So that's what I wanted to find out. So now we know that this is the same as milliliter. Milliliter, a thousand milliliters. But here we have meters. We need to convert meters to centimeters. Because this is the same as 10,000 centimeter cubed. So we need to convert this to centimeters so that we work with the same unit, centimeter, centimeter cubed. There will be one and the same. Now, they want to know how deep it means height, right? So we add the volume of this circular reservoir, which is pi r squared times height. And we are told that the diameter we need to convert 30. So that's the other thing we need to convert 30 meters to centimeters. So that is the length conversion. 30 meters to centimeters. So we have 30 meters because it's from big to small. We multiply by 10. Therefore, it means it is similar to multiply by 100. We multiply by 100. It should be 3,000 centimeters. So now, if we know that we have the 3,000 or 300. I think it's 300. We multiply by 100. So it's 30. No, it's 30 meters to centimeters. So we multiply by 1,000. Yes, it's right. It's 3,000. So now, let's write this. When I write it, yeah, at the bottom. So V is equal to pi r squared times height. Sorry for interrupting. So because the diameter is 30 meters now and we get it on 3,000 centimeters. Do we divide it by 2? Yes, because we need to find the radius. So the radius will be 3,000 divided by 2. Which is 1,500. And then now, we are told what the capacity is. It's 10,000. We're going to use the same unit. So it's 10,000 cubic meters. So it's 10,000 is equals to pi times 1,500 squared. And h is what we don't know. So dividing this side by pi of 1,500 squared. And divide this side by pi of 1,500 squared. So this side and that will cancel. And you'll be left with h of equals to 10,000. So we're going to use calculator. So we have 10,000 divide by pi times 1,500 squared. And the height is equals to 0.0014. Am I calculating it right? I got 0,0014147106. And this will be in centimeters. So if I need to convert it back to meters, I need to divide. Divide. Because we multiply, convert from is 30 meters equivalent to 3,000 centimeters. And that's 30 meters is equivalent to 3,000 centimeters. And we divide the bed by two, which is 1,300, 1,500. If we convert it to meters. And did we convert correctly? 1 cubic meters is equivalent to 1 milliliters, which is equivalent to 1 kilo liters or 1,000 kilo liters. It is equivalent and we said. Ma'am, there was another conversion table that you showed us in the beginning of the session that showed us how to get from millimeters to centimeters. Yeah, but yeah, so when we get from millimeter to centimeter, we divide by 1,800. When we get from centimeter to millimeter, we multiply by 100. That's why we multiply 30 by 100, 3,000. So now we're going to convert from centimeters back to meters. Yes, now I am. I don't want to go back there, but I want to double check the cubic, this kilo liters. Yeah. Right. So we said one kilo liter is equivalent to 1 centimeter cube. Yeah. That's why we said. No, sorry. Go back to Google. So it says one kilo liter. So if I have 10,000 kilo liters, it says it's equivalent to 10,000 cubic cubic meters. Oh, cubic meters, not cubic centimeter. I think I wrote the cubic wrong. Did we do the whole summer wrong? Not really. So what is, how do we write cubic meter? Cubic meter is m cube, right? Yes. So it means yeah, we did this one wrong here. It's one m cube. So if it's one m cube, oh yeah. One m cube is equivalent to 1,000 liters. Then if 1,000 liters is equivalent to one meter cubed cubic meters and therefore then what will be? And we know that one liter is equivalent to 1,000 centimeters, right? But not to centimeter cubed, but not to meter cubed. So we need to be able to convert from meter cube to centimeter cube. How do we convert there? Let's see. Meter cubed, centimeter to centimeter cubed. So one meter cube. Okay, I've got it. One meter cube is equivalent to a million. It's equivalent to one million centimeter cubed. Okay, so it means we need to go back there. We didn't do the conversion right here. So this should be equals to a million centimeter cubed. Centimeter cubed. And therefore it means yeah, we divide it by a million centimeter cubed. And that's hence our answer here will change. This will be a centimeter cubed and this will be centimeter, oh sorry, inside. Yeah, it will be centimeter, then it will be squared. And that will convert to centimeters squared and it will say three minus two will be centimeters. So if a, that's why, and in the exam you will need to know these things by how to convert from one unit to the other, which is very difficult you can see. So I wish you all the best of luck. One million divided by, one million divided by times 1,500 squared, which is then equals to 0.14. And this will be in centimeters. And if they want you to bring it back to meters, then you will say it is equivalent to if we take it back to meters. So this will be centimeters to meters. We got the answer of 0.14. It will be 0.0014 height, which will be very small height. Okay, so that is how you, oh no, no, I didn't divide by a million, sorry, I bet, what's wrong with me. So that won't be one zero comma because I didn't. Ma'am, how did you get the loss or how are we going to convert it from the centimeters to the height? Because it's, wait, let's get the answer right because I also got the answer wrong now. So the answer should be one million, not 100,000, but a million divided by pi times 1,500 squared. And then the answer is... Yes, I did get it right, sorry, my bad. Yes, you did, 0.14, right? Yes. So that's the answer, 0.14. Yes, so it will depend on whether they did ask you that the answer in the options is it in centimeters or is it in meters. So if it's in meters, then you just convert it to meters because it's height. Height is either in meters or centimeters. Oh, okay, okay, I get it. Okay, thank you so much, ma'am. No problem, you are welcome. And that concludes today's session. The next session we're going to be dealing with ratios and proportions. If you have any questions, feel free to ask. We are over with 10 minutes. I just want the conversion tables to study them. Is there any way I can get those? They are on the notes. Just stay on the line right now. I just need to stop the recording. Stay there. Let's close the recording before Melissa kills me.