Mensuration | Step-by-step explanation| evening 11 | GMats Hub

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[00:03:58]Okay. Please, can you hear me? Can you hear me now?

[00:04:08]Hello? Can you hear me now?

[00:04:12]Can you hear me?

[00:04:14]Yeah. Let me know if you can hear me.

[00:04:35]Okay guys, you're welcome to class again. All right, so um I'm trying to fix one or two things. Okay, so um um today we are going to continue from where we stopped the last time. Don't forget the last time um we introduced to us solid shapes. Okay. So we look at common solid shapes. So we look at Qoid and so on.

[00:04:58]All right. And what we able to do the last time was to derive the formulas.

[00:05:04]All right. So if you missed the last class, make sure you get it and make sure you watch the last class because how we derive all those formula was explained in details. All right? So you don't need to cram formulas because you have a lot of formulas to deal with. So once you get the formula you don't have any problem. You understand how the formula um is derived. The reason why many students have problem with this is because of they need to cram a lot of formulas. They don't really understand um the idea of the formula. So once you don't get that you'll be having issue because you have crammed the formula. So make sure that you watch uh the video the last video um I did yesterday. All right. So it's going to be helpful. All right. So now we are going to continue from where we stopped the last time.

[00:05:54]Don't forget as you joining the class, greet the whole class. Say hi. Okay. And don't forget to tap the like button. You are new on this channel. You have not subscribed. Make sure you subscribe to this channel. All right. Okay. So um I want to believe you have your viral your um notes and your calculator of what we got tableable close to you. Make sure you have that because um you are going to be doing one or two things for me today. All right. So now let's start with the first question here. So I'm going to do this one. Now let's look at it. Now a rectangular tank is 70 cm long, 30 cm wide and 20 cm high. So we have to find the number of liters of water that it can hold.

[00:06:42]All right. So a rectangular tank will look like this.

[00:06:50]Okay. Just like a boy. All right. So all right. So this is what it's going to look like. All right. So we want to know the volume of water that this tank is going to contain.

[00:07:06]That's what the question is asking for.

[00:07:08]Now look at it. We have been given that um the length is 7 cm and the wideness is 30 cm while the depth which is the height now is 20 cm.

[00:07:27]So the question asks you to find the volume in lit. Now let's get the volume in cm cube. So that's the first thing we're going to do. Now don't forget the formula for finding volume of aboard.

[00:07:39]This is a cubo. Okay. So the formula is b = lbh.

[00:07:47]All right. The length, the breadth and the height. So now let's plug in the values. So we have the volume = to 70 * 30 * 20.

[00:08:01]All right. So let's multiply everything.

[00:08:04]7 * um 3 that's 21. 21 * 2 that is 42.

[00:08:11]So that's 42,000 cm cube.

[00:08:18]All right, you get that now. So this is the volume of water that this um tank is going to contain. Now but what is the question talking about? The question wants you to get the capacity of this tank in liters not in cm cube. So we need to convert our answer to lit. All right. So I must know the relationship between lit and cm cube. So now how many cm cube make one liter? All right. So if you know I want to drop that in the comment section. How many cm cube make one uh liter?

[00:09:00]Make one liter. How many cm cube make one liter? Okay. Can you drop that in the comment section if you know? All right. So if I didn't see any answer, so we just continue. I will tell you what it is. Yes. Is anybody giving us the answer? How many cm cube make one liter? Okay, nobody is giving us the answer. So that means I have to do that. Okay.

[00:09:27]All right. So, uh now 1,00 1,000 cm cube will give us one liter.

[00:09:41]Okay. To give us one liter. That is it.

[00:09:45]All right. So now one liter will be what? So I cm cube 1 cm cube now is going to be 1 over right you just divide both sides by 1,000. So 1,000 l.

[00:10:03]Okay. So now we want to know what is 42,000 cm cube in liters. So that means 42,000 cm cube is equivalent to 2 42,000 over 1,000. So that's going to be lit.

[00:10:28]All right. So this one cancel this. So we have 42 L.

[00:10:35]So this is the volume of water that this um tank can contain. So that's the answer. Yes. Any question based on what you have just done? Any observation? So raise an observation based on what you have done. So if there's no observation, we move down to the next. So please ensure that you say hi. Say hi. As you're watching, make sure you say hi.

[00:11:01]you greet the class and don't forget you tap the like button make sure you do that okay now let's move down to the next question now I have another question here right let me see is there any observation any question based on what we have done or no all right so no question let's move down to the next Okay.

[00:11:39]Find the volume.

[00:11:45]Find the volume of the solid for the solid blue.

[00:13:03]Okay. Now, can we look at this uh problem on the board? So how do we solve this? The question ask to find the volume of the solid below. So this is the solid. Now look at it. When I was explaining um how we derive the formula for prism, I told you the cross-sectional area times the height that gives the volume of a prism.

[00:13:25]Example of a prism is your cylinder.

[00:13:28]The cross-sectional area of the top of a cylinder is a circle. So we say p<unk> r² * h. That gives us the volume of a cylinder. The same thing also applies to your cool that we just did. Now the cross-sectional area which is a rectangle times the depth. All right. So now this another one here is also a prism. So the cross-sectional area here times the depth. Now the depth in this case now is going to be 20 cm. So I need to get this crosssectional area. So now let me bring out the diagram that will help me. Now the front of this um prison. Let me bring it out. Now it's like this.

[00:14:19]So this is 6 cm.

[00:14:22]This is 5 cm. And you know this length here is same thing as this. So this is going to be 2 cm.

[00:14:30]All right. Okay. So now we want to get um we want to get this is rectangle. So we want to get the area of this thing. Now when you look at this plane shape now this is um um the trapezium because this side will be par to this.

[00:14:54]Okay it's going to be par to this. So this side is par to this. So now to get area of a trapez you know the formula we've done that in shape. So a = 1 / 2 a + b * h why a and b are the two par sides and h is the distance between the two par sides. Okay. All right. So now um here in this diagram now a is 2, b is 5 and h is 6 cm.

[00:15:31]All right. So let's plot that into this formula. So we get the cross-sectional area of this u of this solid. So we have area = 1 / 2 2 + 5 and 6 right. So now this gives you um um 1 / 2 * this is 7 * 6 you get that now. So 2 goes here 1 2 goes here 3. So we have 3 * 7 that's 21 cm².

[00:16:11]So this is the area here.

[00:16:14]All right. So now the next thing now is to use the area here the cross-sectional area to calculate. You multiply that with the depth. So that gives you what?

[00:16:24]So we have volume.

[00:16:26]Volume is the cross-sectional area time the height and that is 21 * the height.

[00:16:35]What is the height? 20. So we have 20.

[00:16:38]So and that gives you what?

[00:16:41]420 cm cube.

[00:16:46]All right. So this going to be the volume of this solid. So suppose the question asks you for the volume in lit.

[00:16:54]So just divide this by 1,000. That's going to give you 0 0.42. Okay. So that is going to be in lit. So if I'm correcting it to lit now, so it's going to be 0.42 liter.

[00:17:10]So that's it. All right. So I hope you all get that. So um any question before I move down to the next uh thing?

[00:17:27]All right.

[00:17:29]Okay. Who is asking Sophia? Okay. Um, what level?

[00:17:40]Once you're in senior secondary school, the question is meant for you, right?

[00:17:45]Everything we are doing here is for senior secondary school. So once you understand what we are doing in senior secondary school so you should not have any problem.

[00:17:57]All right. So that's it.

[00:18:01]Okay. So now let's move down to the next question. So you're in SS1, you're in SS2, you're in SS3. So this class is meant for you.

[00:18:11]All right.

[00:18:34]Okay, the next example we have if if the volume In bedtime, Okay. All right. Um great student let's see how do we solve this problem. Now if the volume of a rectangular base pyramid is 70 cm square and its base area is 28 cm square. Okay. You have to calculate the height of the pyramid. All right.

[00:20:19]Can I give you just like a minute to attend to this question? So you have the formula with you. Can you try that? Let me just give you a minute. Let me see what you going to do. So if you have the answer you can drop that in the comment section. Okay. So you have to be fast about it because I want to solve this question very fast. So um this question is under um pyramid.

[00:20:45]It's under pyramid.

[00:21:12]So this question is under parame. All right, Miss Sophia or Mrs. Sophia. All right, I can see what you dropped there. Your child is in um basic six. All right, this a little bit um advanced to that class. All right, because what we are doing now um at least the student should be in basic nine upward.

[00:21:39]Basic nine upward. All right. Okay. So that's it.

[00:21:48]All right. So um yes, anybody with uh an answer to that before.

[00:22:01]Okay, nobody's dropping an answer. I have to move very fast. Let's solve it together. So we move down to the next thing. Now if the volume of a rectangular base pyramid is um 70 cm square. So we have been given the volume volume of pyramid to be 70 cm cube and it base area is 28 cm squared. So base area so we have been given the base area to be 28 cm square.

[00:22:42]Now the question is to calculate the height of the pyramid. It's very easy.

[00:22:47]So all is I need to know is the formula for calculating volume of a pyramid. So once I know the formula so I just plug in the values and I get the height. Now let's look at it. So volume of finding volume formula for finding volume of pyramid is 1 3 base area time I so this the formula okay so now the volume has been given to be 70 in the question 1 / 2 3 sorry time the area that's 28 that has been given in the question so times the height okay so Now let's try and simplify. So this is 70 = 28 / 3 h. So here you can divide both side by co of h. So that is going to give you what? 70 * 3 over 28 = to h. You get that? So once you divide both side by fraction once it comes to this other side. So the denominator turns to numerator while numerator to denominator. So now can we break this one down? Now two goes here is 35 and and the two goes here is 14. Right?

[00:24:06]Okay. So um seven goes here is two. 7 goes here is five. All right. So that means h now is going to give us 5 * 3 that's 12 uh 15 / 2. So h is going to be 7 number 1 / 2 cm or you write h to be 7.5 cm. So so this is the answer to this problem. All right. So I hope you understand that. Okay. So any question based on what we have done I'll move it down to the next question. Any question?

[00:24:46]Any observation?

[00:24:48]All right.

[00:24:52]Okay. So, let's move down to the next thing.

[00:25:22]Next example we have the density density of copper.

[00:25:38]Copper used for The spherical is 8.9 kilome kilog per me cube.

[00:26:01]And the radius the radius of the ball is 3.5 cm.

[00:26:18]Calculate.

[00:26:22]Calculate the curve surface area, B volume, and C mass of the sphere.

[00:26:48]we have = 22.

[00:26:51]Okay. So now can we all see the question? So um you can read in between lines and see does it look like what you can solve?

[00:27:07]All right. So um now let's do this one together.

[00:27:11]Let's do this together.

[00:27:14]All right. Now the density of a copper used for a spherical ball is 8.9 kg per me cube per me cube and the radius of the board is 3.5 cm. Now calculate the curved surface area two the volume three the mass of the sphere.

[00:27:40]Okay. So now can you see the three things we asked to do? All right. So now let's start with the first one. We are to calculate the C surface area. Now C surface area of what? Off a spherical ball. So I need to know the formula for calculating off surface area of a sphere. All right. So now make sure you go through my last video, the one I did yesterday. So I explained all those formula. All those formulas are there.

[00:28:13]So you must have the formula at your disposal and you understand how those formulas have been derived. Okay. Curve surface area of a sphere is 4 pi r² right 4 pi r² that is the co now. So you just plug in the values. We have 4 * 22 / 7 * now the radius is 3.5.

[00:28:44]So we have 3.5 * 3.5.

[00:28:49]You get that now. So 3.5 goes here 1.

[00:28:52]3.5 goes here is 2. 2 goes here 1. 2 goes here is 11. So we have 4 * 11 * 3 Okay. So, and that is the same thing as 44 * 3.5.

[00:29:14]Okay. So, let's multiply these two. What do you have when you multiply the two?

[00:29:19]Let's see. We have 44 * 3.5. So, 5 * that's 5 * 4 is 20. 5 * 4 20. So, that's 24. Okay.

[00:29:34]Now 3 * 4 that's 12 3 * 4 12 12 so we have this 0 um 6 5 1 so the answer is going to be 156 156 and what's going to be the unit is going to be in cm squared so that is it do you understand that now So we have gotten the C surface area of this um spherical ball.

[00:30:09]Now the next question is we have to find the volume. What is the volume of this sphere? So now we have formula for finding volume of a sphere is 43 pi r cube. You get that now? So now let's plug in the value. So we have 4 / 3 * 22 / 7 * what is um the radius? 3.5 * 3.5 * 3.5.

[00:30:41]You get that now? So um um 3.5 goes in 7 that's two. 3.5 goes here that's one. So 2 goes here 1. 2 goes here 11. So what we have here now is 4 * 11 * 3.5 * 3.5 everything all over 3. Can you evaluate that? Now try that and drop the answer the comment section. So when you multiply and you divide by 3.

[00:31:11]So um that's 44 * 3.5 square. All right. So, and that by three. So, what do you have? So, here what I have here now is anybody with the answer, let me see. Is anybody giving me the answer? So, what's the answer to that? Okay, you are still working on it.

[00:31:36]All right. So, what I have here now is 179 179.67 cm cube. All right. So that is the volume. So we now have the volume for this. So now let's put this one down.

[00:31:55]Volume is 179.67 cm. Okay.

[00:32:05]Now let's move down to the last part of the question. Now the question asks us to find the mass of the sphere. We want to get the mass of the scale. So how do we get mass of the sphere? When you look at the question, we have been given one parameter here that is the density. So, um I need to know the formula for density. Density is mass over volume. Mass over volume. That is the formula for density. So, density density equals to mass over volume. So you can write this formula down in your jar. So you take note of it. So the formula for finding density of a material. So it's um mass over mass of the material over the volume. So that give you density. So but in this case now we are not looking for density. We want to get the mass of that spherical ball. So you have mass will be equals to density time volume. So that's what you're going to have. You get that? Okay. So now but there will be an issue. Now what is the issue? Now when you look at the unit of the density given now is in kilome kilogram per meter cube. But look at the volume we have is in cm cube. So there will be an issue. So what I need to do here now is I will convert this um volume in cm cube to me. So there will be consistency in units.

[00:33:53]All right. So now let us convert this.

[00:33:56]So now I now begin to ask myself how many um cm cube makes um me cube make 1 m cube. So now let's see 10 power of 6 cm cube same as 1 million will give us 1 m cube. So make sure you master this. So you are supposed to be familiar with this 1 million cm cube.

[00:34:32]Make one me cube.

[00:34:37]All right. So now in this case now we want to convert this volume to me cube. So that means we are going to divide this by 10^ 6. All right. We are dividing by 1 million. So that means um volume volume volume in me cube is 179.67 over 10^ 6. Okay. So this is going to be me cube now. So this is me cube. Okay.

[00:35:15]So having this now we can now find the mass.

[00:35:20]All right. So we now say mass is the density that's 8.9 time the volume 190 79.67 67 over 10^ of 6, right?

[00:35:43]Okay. So now what do we have? We do that. We have 8 9 * Now let's divide this by one. Just move the point six times. So that's going to be 0.017 967.

[00:36:03]Okay.

[00:36:08]Okay. So, 1 2 3 4 5. Okay. I think you need one more zero. Okay. All right. 1 2 3 4 5 6. All right. So, so when you divide by 1 million. So, this is what you're going to have. So, just use this to multiply this and let's see what you're going to have. Okay. So um 8.9 time please try and compute that over there.

[00:36:48]So let's see what we have as your answer.

[00:36:54]Okay. So um I've gotten my own answer.

[00:36:57]So mass is there anybody with the answer?

[00:37:02]the mass. So what do you have when you multiply?

[00:37:08]Okay, thank you divine. So do you have the answer?

[00:37:13]Okay, so make sure you are completing something. You are doing something. Make sure you are participating. All right, so we have 1 9 59 999 cm.

[00:37:29]Okay, sorry. that's going to be in kilogram.

[00:37:34]So that's what we have.

[00:37:36]So now let's correct this to 3SF 1 2 3.

[00:37:42]So that is approximately 1.6 kilog 3.

[00:37:53]So this is going to be the mass of the spherical um ball.

[00:38:02]Yes. So that is that. Any question based on that? If you have any question you can uh drop that in the comment section.

[00:38:10]Let me see before I move down to the next question. Any question? Is it well understood?

[00:38:18]Yes.

[00:38:24]Right. Well done. Okay. Thank you, Rajie. Thank you. You're welcome. Yes.

[00:38:30]What you just saw now, is it well understood to see? Is it well understood?

[00:38:37]All right. Thank you, Divine. Okay. So, Divine said we should go on. That means it's well understood. All right. So, I want to believe it applies to others as well. Okay. Now, can we look at another question?

[00:38:51]Let's look at another question.

[00:39:23]Okay, this is a sphere.

[00:39:29]a square has a volume of 200 cm cube.

[00:39:42]What is the volume of the seps?

[00:40:34]Okay, this is another interesting question. Yes. Can you see this question, please? I want you to read in between lines and tell me the answer to that problem. Yes. If you can find the solution to that problem, drop it in the comment section. You got if you get the answer, I clap for you here. Right. Let me just give you a minute now to attend to the question.

[00:41:00]All right. So now reading between. So a sphere has a volume of 200 cm cube. What is the volume of a second sphere whose radius is a quarter of the radius of the first ball?

[00:41:16]All right. Okay. So that's it.

[00:41:21]Can I give you a minute to try to try this?

[00:41:39]Okay. So, um let's let's solve the problem together because of time. So, let's do that together because of time.

[00:41:49]So, you can compare with what you are doing. So, by time we start solving.

[00:41:53]Now, look at the problem. Now a sphere has a volume of 200 cm cube. What is the volume of a second sphere whose radius is a quarter of the um radius of the first ball? Now the first thing I need to do now is let me get the radius of the first sphere. So you know two things are being considered here. Now they talking about two sphere.

[00:42:21]One is big and one is small. Now and the bigger one have a radius R.

[00:42:29]Now the question now is saying that the second one which is small the radius is quarter of this that is to say if this one is four this one is going to be one.

[00:42:40]The radius is going to be one. So if this one is eight the radius here is going to be two. So that's what the question is saying. So whatever you have as radius here divided by four is going to be the radius of the second one.

[00:42:55]That is it. So you now have the idea of the question now. So now let us find the radius of the first one. So once you get the radius of the first one. So we just divide it by four and put it inside the second um sphere because the second sphere have a radius of 1/4 of that of the first one. So now we know the formula for finding volume.

[00:43:24]Volume of a sphere 4 r cube.

[00:43:31]All right. So this is the formula. So here now we have given the volume to be 200. Let's plug in 200. We want to get this r. So we have 4 4 pi r c over 3. So you can write it this way. All right. So now let's cross multiply. If you cross multiply you will have 600 = to 4<unk> r cube. So let's divide both sides by 4 pi. So we now have 600 / 4 pi.

[00:44:12]4 pi. That is r.

[00:44:15]Don't forget what we want to get now is.

[00:44:19]Okay. So now um four goes here one four goes here is 150. So this is 150. So 150 / pi = to r.

[00:44:35]So I can now get the answer for the um for the radius radius of the first sphere. So just take cube root of both sides. So I have cube root of 150 / pi = to half. So that's what you have.

[00:44:53]You get that? So now the second sphere I want to get the the question asks me to find the volume. The question say what is the volume of a second sphere whose radius the radius of the second sphere is a of the radius of the first sphere. Do you understand that? So now let's get the volume. Now before we get the volume let us get the radius. Now let's call that radius let's say radius um r2 to be equals to radius of the second step.

[00:45:38]Okay.

[00:45:42]So um we can now go ahead now and get um the volume can get the volume of volume of the second sphere. But then have we gotten the R? So we have R2 is what? 1 / 4 1 / 4 of this cube root of 150 / pi.

[00:46:18]You know this is the radius of the first one. So the radius of the second one is 1/4 of okay 1/4 of the radius of the first one. So this is the radius of the second sphere. So all right. So I'll now write the volume volume of second sphere will be equals to you know that's 4 / 3 by r c you get that so we have 4 / 3 *<unk> * the volume look at the volume this one should be r2 you get it now so r2 is 1 / 4 cube root of 150 / pi. So everything raised to power. Do you understand now?

[00:47:10]So we have just replaced R2 with what we have here. Can you see that now? So we plug in the value of R2. So that's what we have here. So now we have 43 * 5 * Now we multiply each of them by themsel three times. So this 1 / 4, I'll multiply it by itself three times. So 1 / 4 * 1 4 * 1 / 4. So that's going to give me 1 / 64 cuz 4 * 4 is 16. 16 * 4 is 64. Okay. So that gives me 1 / 64* now I will multiply this by itself three times. So it's as good as just saying this one will cancel this. All right?

[00:48:01]Because this one is more like 1 / 3. So when you multiply that with this cancel out okay so now you have 150 / pi.

[00:48:14]All right. So now can we simplify? You can see this one will cancel this here.

[00:48:18]So uh 3 goes here 1. 3 goes here is 50.

[00:48:23]All right. So four goes here one four goes here is 16.

[00:48:29]All right. So then we now have um we can still simplify further. Two goes here is um 8. 2 goes here is 25. So you have 25 / 8. That's going to be the volume. So you can simplify further. So that is t number 1 8 cm cube. So this is going to be the volume of the second sphere or you write it like this. You want to write it in decimal that's 3.125 cm k. So this going to be the answer to the problem. All right. So any question based on what we have just done? The volume of the second sphere. Any question based on what we have done.

[00:49:27]Okay. So if there's no question based on what we have done. All right. So we are going to be hanging it here today. So we going to be rounding up the class here today. So tomorrow is another day. So we are going to go further.

[00:49:42]into um questions on meation and uh tomorrow we are going to be looking at um some technical questions. Okay. So make sure that you you around for the class. All right. So if you have not subscribed, make sure you do that because you will not be notified if you are not if you are not if you didn't subscribe. So make sure you subscribe. All right. and uh make sure you inform your friends, let them know about the class, let them come in. Okay?

[00:50:15]So uh thank you very much those of you that started with me from the beginning down to this period where we stopped. So I thank you very much for those of you that are just joining the class for the time. You are especially welcome. Right?

[00:50:31]Okay. So I'm happy, I'm excited, I'm glad seeing you. Thank you very much.

[00:50:36]Bye-bye.

[00:50:52]Okay. Thank you, Divine. Yeah. Thank you. God bless you, too. God bless you.

[00:50:59]Thank you for appreciating me. All right. Uh Darasimi, thank you. You Thank you for appreciating me. You're welcome.

[00:51:07]Right. Okay. I mean that it's been a while I've seen this person. Okay. Thank you very much. Thank you for thanking me. All right. I appreciate you. All right.

[00:51:45]Oh. Uh, thank you Dasimi foring me.

[00:51:49]Thank you. Um, you're welcome. Um, you're welcome. Thank you for appreciating me. Um also Mutayo, thank you. God bless you.

[00:52:10]Thank you. God bless you. All right, Divine. I really appreciate you. Okay, you're actually participating in the class. I notice you. Thank you. So, All right. I thank you everyone. Thank you everyone.

[00:53:29]Yeah.

[00:53:31]Okay.

[00:53:34]Okay.

[00:53:37]So, those of you that didn't join the class in time, make sure you go through the uh class on the beginning. You can go through the class and um let's see.

[00:53:50]So, um thank you. Thank you. You're welcome. God bless you.