Volume of a Prism Answers Corbettmaths

Hi, welcome to this Cormath video. In this video, we're going to look at the video solutions to the CM math practice questions on the volume of prism. If you need any extra help in this topic, if you go to Cor Mavs and go to the videos and worksheet section and scroll down to video number 356, there's dedicated video tutorial there on finding the volume of prism. Alternatively, you could scan the QR code. But in this video, we're going to focus on the video solutions to the practice question. So, let's get started. Okay, so let's have look at our first question. Question number one. So, question number one says, shown below is cuboid. So, we've got this cuboid and we've been asked to find the volume of the cuboid and to include units. So, in this worksheet, we're going to be looking at how to find the volume of prisms such as triangular prisms and things like that where we're going to be finding the area for the cross-section and then multiplying by the length or the height. but also remember that cuboid is prism as well. And you've probably already looked at how to find the volume of cuboid where you would do the length times the width time the height. So, if was asked to find the volume of this cuboid, would just do the volume is equal to the length multiplied by the width multiplied by the height. And if you do the length times the width time the height, you'll get the volume of the cuboid. So, let's do that to begin with. So, the length is equal to 9. We're going to multiply that by the width, which is three, and we're going to times that by the height, which is 2. So, we do 9 * 3, that's equal to 27 * 2 is equal to 54. So, that means the volume of this cuboid is 54 cm cubed. And that's it. That's the volume of that cuboid. 54 cm cubed. Now, just want to also mention that in this video, we're going to be looking at how to find the volume of prism. And to find the volume of prism, we'll be finding the area of the cross-section and then times it by the length of the prism. So here, if we were to work out the area of the front of the cuboid, we would do 9 * 2, that's the height, 9 * 2. And 9 * 2 is equal to 18. And then if we times it by the length of the cuboid and then in this case, that would be three. And if we do 18 * 3, that's equal to 54 as well. So you could use that approach where you get the area of the cross-section and times by the length. But if it's cuboid, just did the length times the width times the height and that'll give you the volume of the cuboid. Okay, let's have look at our next question. Question number two. Okay, question number two. Question number two says, shown below as cube. So we've got this cube and we've been asked to find the volume of the cube and to include units. So again, we could get the area of the front of the prism. So here we could do 5 * 5 to get the area of the front of the cube, which would be 25 cm squared and then times by the length. So times 1 over 5. But if it's cube, would just tend to do the volume is equal to the length time the width time the height, which would just be in this case 5 * 5 * 5, which is the same thing really anyway. 5 * 5 is equal to 25 * 5 is equal to 125 cm cubed. So that's the volume of that cube. 125 cm cubed. And the units are centimeters cubed. And that's it. So to get the volume of cube, you just do the length times the width times the height. And because it's cube, they'll all be the same value. So here it just be 5 * 5 * 5 and 5 * 5 is equal to 25. And if you need to do 25 * 5, you could just do it to the side and do 25 * 5 by doing 5 * 5 is equal to 25. Put five down and carry two. And 5 * 2 is 10 + 2 is 12. So you could just do the method if you need to. knew that 5 * 5 * 5 is 125 because it's cube number. 5 cub is 125. Okay, let's look at our next question. Question number two. Okay, question number two. So we've got on to these nice triangular prisms. So really like these questions here where it says shown below as triangular prism. So we've got this triangular prism and we've been asked to find the volume of this triangular prism. So to find the volume of triangular prism like this, we want to get the area for the cross-section. So if you have look at this, we've got this triangular prism. If you chop it down vertically here, every time you chop it down, you'd have this identical this congruent triangle, this identical triangle the whole way down through this prism if you cut it anywhere vertically down this way. So we want to find the area of this cross-section. the area of this triangle at the front. And if we find the area of this triangle at the front, that'll be the area for the cross-section of the prism. And then you just need to times it by 12, the length of the prism. So let's find the area of this triangle. To find the area of triangle, you do the base time the height divided by two or half the base times the height. So the area for the cross-section area of the cross-section or the cross-sectional area you may see is the area of this triangle. So we would do half the base times the height. That's how you find the area of triangle. Half the base times the height. Now you could do the base times the height and then half it. You could do half the base and then times by the height. You could do half the height and then times by the base. I'm just going to do the base times the height first of all. So I'm going to do half of and 5 * 4 is equal to 20 and then we're going to half it. So half of 20 is equal to 10. So that'll be 10 cm squared. So the area of this triangle would be 10 cm squared. And it's very important you know how to find the area of triangle if you want to find the volume of prism. So know how to find that area of that triangle. So you do the base time the height and then half it or half the base times the height or half the height times the base. We're making sure you're just half and once. So the area for this triangle, the cross-section is 10 cm squared. If we want to find the volume, we're now just going to do that area multiplied by the length of the prism. So we're going to do 10 * 12. So 10 * 12 is equal to 120. So the volume of this prism would be 120 cm cubed. And that's it. So we just times that cross-sectional area, which was 10, by the length of the prism, which is 12. And 10 * 12 is 120 cm cubed. And that's it. Okay, let's look at our next question. Question number four. So question number four says, shown below is prism. So, we've got this pentagonal prism because we've got this pentagon at the front and then it's prism. So, it's pentagonal prism and the cross-section here is shaded. It's shaded in green because if you chop it down anywhere vertically, you'd get that identical pentagon. You'd get that congruent pentagon. And it says the cross-sectional area is 21 cm squared. So, it's quite nice. It's told us the area of this cross-section, the area of this green region to be 21 cm squared. And then we're told the prism has got length of 6 cm. I've been asked to find the volume of the prism. Well, actually, this question is really, really nice because we know the cross-sectional area. So, to find the volume, we just need to take the cross-sectional area, which is 21, and times by the length of the prism, which is six. So, we just need to do 21 * 6, and that'll be the volume. So, it's already worked out that area for us. Quite often, we have to work out that area, like in the last question, but this time, it's been given to us. So, we just need to do 21 * 6. That's non-cal question. So, 6 * 1 is 6 and 6 * 2 is 12. So the answer would be 126 cm cubed. So that's the volume of that pentagonal prism. So the volume of that prism is 126 cm cubed. Okay, let's look at our next question. Question number five. Okay, question number five. So question number five says the diagram shows trapezoid prism. So it's trapezoid prism. We've got this trapezium and it's prism. So it's trapezoid prism and we're told the area of the cross-section, so the shaded area is 55 cm squared. that the area of this face here is 55 cm squared and the volume of the whole prism is 330 cm cubed and we've been asked to find the length of the prism. So we want to find the length of the prism. So if we wanted to find the volume we would take the cross-sectional area which is 55. You times that by this length. You times it by whatever the length is and we would get an answer of 330. So, we just need to figure out what they've multiplied the 55 by to get 330. And that'll be the length of the prism. So, let's see how many 55s go into 330. Now, it's non-calculated question, so that means that I'm thinking it's going to be quite nice number. So, let's write down the multiples of 55. So, they would be 55. Adding number 55 would be 110. Adding number 55 would be 165. Adding number 55 would be 220. Adding number 55 would be 275. And again, if you need to do any of these additions, you could do it on the page here. Adding another 55 will be 330. So that's fantastic. It's 1 2 3 4 5 6. So 55 * 6 is equal to 330. So that means that this length here must be 6 cm. So the length of the prism is 6 cm. And that's it. Okay, let's look at our next question, question number six. So question number six, we've been given diagram of prism. So we've got this prism, this L-shaped prism, and we've been asked to work out the volume of the prism. So, we want to find the area for the cross-section. So, the cross-section is this shape here. I'm just going to highlight it here. So, this is what we want to find the area of. That's the cross-section. So, we want to find the area for the cross-section. And then we're just going to times it by 10, the length of the prism. So, let's find the area of this shape here. So, we're going to divide it. I'm going to split it into two rectangles. So, here we've got smaller rectangle here that is 5 cm by and then if we have look here, we've got three. So, that'll be three there. So, this part is going to be 5* 3. This area is going to be 5 * 3 which is 15. So 5 * 3 is equal to 15 cm squared. So that's fantastic. This area is 15 cm squared. Now we want to find this area. The height of this rectangle is 8 cm. But we want to know this measurement here because we need to do 8 * the width to get the area of this rectangle. Now the whole shape has got width here of 9 cm and this is five. So that means that this part must be 4 cm up there because four plus 5 must be equal to 9. and 8 * 4 8 * 4 is equal to 32 cm squared. So that means the area of this part of the shape, this rectangle here would be 32 cm squared. So that means the whole front of the shape, the whole cross-section here has an area of 32 + 15 is equal to 47 cm squared. That's the area of the cross-section. 47 cm squared. Now we've been asked to find the volume of the prism. So to find the volume, we take the area of the cross-section, which is 47, and you times by the length of the prism, which is 10. So 47 * 10 is equal to 470 cm cubed. So that's the volume of the prism. 470 cm cubed. And that's it. So let's write that down. 470 cm cubed. Okay, let's look at our next question. Question number seven. So question number seven says, shown below is prism. So we've got this L-shaped prism, and we've been asked to work out the volume of the prism. So we want to find the volume of this L-shaped prism. So we want to find the area of the cross-section. So this shape and then we'll times it by the length of the prism, which is 4 in this case. So we want to find the area of this crosssection here, this shape. Okay. So we want to find the area of this shape. So what I'm going to do is I'm going to cut this shape into two rectangles. So I'm going to cut it down this way. So we've got this rectangle here and this rectangle here. And if we find the area of both of these rectangles, we can add them together to get the area of the cross-section of the prism. So let's start off with this rectangle here. So we've got this length to be 6 That means that this length here is 6 That's six. And if this length is 9 that means that this length is 9 That's 9 there. And 9 * 6 is equal to 54 2. So the area of this rectangle is 54 squared. Now let's find the area of this rectangle. So if this length is 3 that means that that length is 3 And if we do 3 * 10, that's equal to 30. So 30 2. So that means the area of the front of this prism would be 30 + 54. So 30 + 54 is equal to 84 squared. So that's the area of the front of the shape, the area of this shape, which is the cross-section of the prism. Now we just need to multiply the area of that cross-section that 84 squared by the length of the prism, which is four. So the volume would be equal to the cross-sectional area, which is 84 squared, multiply by the length of the prism, which is four. And if we do 84 * 4, that'll give us the volume of the prism. So let's do 84 * 4. So 4 * 4 is 16. Put six iron in carrier 1. 4 * 8 is equal to 32 + 1 is 33. So that means the volume of this prism would be 336 cubed. So that's the volume of this prism. Okay, let's have look at our next question. Question number eight. And so question number eight says, shown below is triangular prism. So we've got this triangular prism. So we've got this triangular cross-section here. So this is the cross-section of the prism. of this triangle and then the length of the prism would be 10 cm. So we've been asked to find the volume of this triangular prism. So we want to find the area of this cross-section, the triangle. And once we find the area of the cross-section, we can then multiply by the length of the prism, which is 10 cm. So let's find the area of this triangle. To find the area of triangle, the area of triangle is equal to half the base times the height. So we're going to do half of the base times the height. So that's going to be 7* 3. Now remember, you could do half of seven, which is 3.5, and then times it by three. Or you could do half of three, which is 1.5, and then times that by 7. But think much easier approach for this question would be to do 7 * 3, which is 21, and then half it. So 7 * 3 is 21. So we're going to do half of 21, and half of 21 is 10.5 cm squared. So that's the area of that triangle, 10.5 cm squared. Now, to find the volume of this prism, we need to get the cross-sectional area, which is 10.5. And we just need to multiply that by the length of the prism. And the length of the prism is 10. So, we're going to times that by 10. And 10.5 * 10 would be 105. And then, let's remember our units. We're dealing with centimeters here. So, that'll be centime cubed. So, the volume of that triangle prism would be 105 cm cubed. And that's it. Okay. Let's have look at our next question. Question number nine. Okay. So, question number nine. It's calculator question. We're told shown below is triangular prism. So, here's another triangular prism, and we've been asked to find the volume of this triangular prism. So, again, we want to find the area for the cross-section. So, we've got this triangle, that's the cross-section of the prism, that triangle there. And we want to find the area of that triangle, and then we'll times it by the length of the prism, which in this case would be 21.5. So, let's find the area of the triangle. So, the area of triangle is half the base times the height. So, half the base times the height. We could do half of the base, which would be half of 6.8 would be 3.4. So, you could do 3.4* 4 * 8.5. Or you could have the 8.5 and then times it by 6.8. But in this case, I'm going to do half off and I'm just going to times them together. So 8.5 multiply by 6.8. So I'm going to times them together and then I'll half it. So I'm going to do half off and then on my calculator can just type in 6.8 * 8.5 and that's equal to 57.8. And then I'm just going to divide that by two. So divided by two is equal to 28.9. to 28.9 cm squared. So that's the area of that triangle which is the cross-section of that prism. Now we just need to times it by the length. So the volume of the prism will be equal to 28.9 multiplied by the length of the prism which is 21.5. So that's the area for the cross-section multiplied by the length. So 28.9 * 21.5 is equal to 621.35. And then we're dealing with centimeters here. So that'll be centimeters cubed. That's the volume of that prism. So just to recap, we find the area for the cross-section, which was 28.9. And then we multiply that cross-sectional area by the length of the prism, which is 21.5. And then we've got the volume. That's it. So we just find the area of the triangle and times how long the prism was. Okay, let's have look at our next question, question number 10. Okay, so question number 10. This time we've got trapezoid prism. So we've got this trapezium, which is the cross-section of the prism. So if you chopped it down vertically, you'd always get that trapezium. So we've got this trapezium and the length of the prism is 12 cm. And we've been asked to find the volume of the prism. So we want to find the area of the cross-section. So we want to find the area of this trapezium. And then once we find the area of the trapezium, we can then times it by 12 because that's the length of the prism. So let's find the area for the trapezium. So the area of trapezium is half + time the height. So what that means is we do half of plus That's the two parallel sides. So we're going to do 6 + 8. Well, then half that and then times it by the height, the distance between them, which is five. So, we're going to do half of plus So, that's going to be 6 plus 8. So, 6 + 8, the two parallel sides. And then we're going to times that by the height of the trapezium, which in this case is five. So, times by five. So, if we work this out, half, and that's calculator question, you could just type that into the calculator and get the answer if you wanted to straight away. 6 + 8 is equal to 14. Half of that is 7. And then we're going to times by 5. And 7 * 5 is 35. So that means the area of that trapezium is 35 cm squared. And it's very important whenever you're doing these questions, you know how to find the area of triangle, which we looked at previously. Half the base times the height, but also trapezium, which is half plus and then times by the distance between them, that perpendicular height. And now we find the area for the cross-section. Now we just need to multiply by the length of the prism. So the volume will be equal to the cross-sectional area, which is 35, multiply by the length of the prism, which is 12. And we can just do 35 * 12 on our calculator. So 35 * 12 is equal to 420. And we're dealing with centimeters here. So it'll be centimeters cubed. And that's it. That's the volume of that prism. 420 cm cubed. Okay. Let's have look at our next question. Question number 11. So question number 11 says, shown below is prism. So we've got this prism and the cross-section is parallelogram. So this is parallelogram prism or prism that has cross-section of parallelogram. So as you can see here, if you cut it down vertically, no matter where you cut it, it will be that parallelogram there. So to find the volume of this prism, we want to find the area of this parallelogram. So we've got this parallelogram. We want to find the area of that parallelogram. And then we'll times by the length of the prism, which in this case is 14. So to find the area parallelogram, that's another shape you need to be able to find the area of. It's just the base times the height. So the length of the base times the height, the distance between the two parallel sides. So in this case the length of the base would be 9 because it's 9 cm in terms of the length of the top of it. That means the base of it would be 9 cm. And then we're going to times it by the perpendicular height. That means the distance between these two parallel lines. So in this case it would be four. This five we don't actually need to use in this question. So the area of the parallelogram will be the base time the height. The base of the parallelogram is 9 multiplied by the height of the parallelogram which is the distance between the two parallel sides which is 4. And 9 * 4 is 36 cm squared. and we don't need to use that 5 cm. Okay, so that's it. We just do 9 * 4. So that's the area of the parallelogram, 36 cm squared. We want to find the volume of this prism. So we're going to do the volume, which is the cross-sectional area, which is 36, multiply by the length of the prism, which is 14. And if we do 36 * 14, that'll give us the volume of this prism. And 36 * 14 is equal to 504. And then the units would be centime cubed. And that's it. So that's the volume of that prism. 504 cm cubed. Okay, let's look at our next question, question number 12. So, question number 12 says, "The solid triangular prism shown below is made from metal." So, we've got this metal triangular prism, and we've got the triangle, which is the cross-section here, and the base of the triangle has length of 40 cm. The height of the triangle is 22 cm, and the length of the prism is 65 cm. We're told that this prism is melted down and the metal is used to make solid cubes and each with side length of 3 cm. So, we want to make lots of these cubes that have got side length of 3 cm. And the question says, how many cubes can be made? So, how many of these cubes can be made from the metal that comes from this shape here? So, if we find the volume of this triangular prism, that'll be how much metal there would be. Then, we could find the volume of the cube and see how much of the metal is needed for each cube. And then we could just divide it the total volume of this shape by the volume of the cube to see how many cubes can be made. So, let's do that. So, let's find the volume of this prism. So, to find the volume of the prism, we're going to need to find the area of this triangle to begin with. So we want to find the area of that crosssection and then we'll times it by the length of the prism which is 65. So the area of the cross-section would be it's triangle. So half the base times the height. So we're going to do half the base times the height. Well we could do half of 40 which is 20 and then times that by 22. That'd be quite straightforward. It's calculator question actually. So you can actually just type this in half of 40 * 22. Or you could do 40 * 22 get that answer and then divide by two. And when you do that, you'd get an answer of 40 * 22 is equal to 880 / 2 is equal to 440 cm squared. So that's the area for the cross-section. Now we want to find the volume of this prism. So we now need to times that cross-sectional area by the length. So we need to times by how long the prism is. So the volume will be equal to 440 multipli by 65. And when we times by 65, we get volume of the volume of that prism is 28,600 cm cubed. So that's the volume of that triangular prism. And then we're told that that prism is melted down and the metal is used to make all the cubes. So altogether the volume of that metal would be 28,600 cm cubed. That's how much metal there would be. And then each of the cubes made has got side length of 3 cm. So let's find the volume of this cube. The volume of the cube would be 3 * 3 * 3. So 3 * 3 * 3. And 3 * 3 is 9 * 3 is 27. So that's 27 cm cubed. So each of these little cubes has got volume of 27 cm cubed. So if we divide the total amount of metal, which would be 28,600, by the volume of each cube, which is 27, we can then see how many cubes can be made. So let's do that. So let's take the volume of metal that we've got, 28,600 cm cubed of metal. Divide that by 27, how much metal is needed for one cube. That tells us how many cubes we can make. So that's equal to, and it's decimal number, 1,59.259. and so on. Now, obviously here, if we look at this, we can't make 1,60 cubes. We can only actually make in terms of complete cubes 1,59. So, 1,59 cubes can be made and there'll be little bit of metal left over and that's it. Okay, let's have look at our next question. Question number 13. So, question number 13, we've got this prism and we've been asked to find the volume of the prism. So, if we have look at this prism, it's trapezoid prism. We've got this trapezium at the front of the prism. So, we've got this trapezium at the front of the prism. Now, some people might look at this and actually cut it into rectangle and triangle. That would be fine as well. But think if was doing this question, would actually just find the area of this trapezium. but you could actually use either approach. You could cut it into rectangle and triangle and then add them together to get the area of the front of the prism and then times it by 20. So, here we've got our trapezoid prism. The cross-section of the prism is this trapezium here. And it's the trapezium. If you turn your head sidewards, you might actually look at it in terms of the trapezium that we've seen earlier in this booklet. But we've got this trapezium here. And then in terms of the length of the prism that would be 20 cm. So we need to find the area of this trapezium and then times it by 20. So let's find the area of this trapezium. Remember the area of trapezium is equal to half + * where and are the two parallel sides. So in this case that would be 24 would be one of them. In terms of this one here that would be equal to 16. So here we've got our two parallel sides shown with the two little arrows. And the length of those two parallel sides would be 24 and 16. and is the perpendicular distance between them. So that straight distance between those two parallel sides would be 6 cm. That 10 cm there, that's diagonal length. We don't actually need that. It's bit of red herring here in this question. So in terms of finding the area of this trapezium, we're going to do half and then we're going to do plus So it's going to be 24 + 16. And then we're going to times that by the distance between them, that perpendicular distance between them, which is six. And when we do that, we get well 24 + 16 is 40. half of that would be 20 and times by 6 would be 120 cm squared. 120 cm squared. So that's the area of that trapezium. 120 cm squared. So that's the area for the cross-section. Now to find the volume of the sheet, we just need to do the cross-sectional area, which is 120 multiply by the length of the prism. And as you can see here, that's 20. And if we do 120 * 20, that will be the volume of this prism. So 120 * 20 is equal to 2,400 cm cubed. And that's it. So that's the volume of that prism. Okay, let's have look at our next question. Question number 14. So question number 14 says, you've got solid glass paper weight. So we've got the solid glass paper weight. It's trapezoid prism. We've got this trapezium at the front and as you can see, it's prism. And we're told the density of the glass is 2.5 per cime cubed. So every single cm cubed of this glass paper weight has got mass of 2.5 And we've been asked to work out the mass of the paper weight include suitable units. So we want to find out how heavy this paper weight is. We want to find its mass. So if we want to find the mass of this paper weight, we're going to need to find the volume of the paper weight. And then once we know the volume of the paper weight, we know that every single centimeter cubed will have mass of 2.5 So we can just times the volume by 2.5, the density, and that'll give you the mass. So let's work that out. So let's find the area of that cross-section. And we have got this trapezium at the front of the prism here. And if we find the area of that trapezium, we can then times by the length of the prism, which is 10. So the area of trapezium is equal to half + * Where and are the two parallel sides. So in this case, two and five. And is the distance between them, that perpendicular distance between them, which is four. So we're going to do half of + So that's 2 + 5 * which in this case is 4. That's calculator question. So that's quite nice. You can just do 2 + 5 / 2 * 4 is equal to 14. Or you can type it in like this. You get that's equal to 14 and that's will be centime squared. So the area of that cross-section will be 14 cm squared. So that's the area of the front of that prism. Now to find the volume of the prism, we just need to times it by its length which is 10. So the volume will be equal to the cross-sectional area which is 14 * the length which is 10 and 14 * 10 is 140 cm cubed. So that's the volume of the paper weight. Now we were asked to find the mass of the paper weight. Remember that every single centime cubed has got mass of 2.5 That's what this density means. That the density of the glass is 2.5 per cime cubed. So every centime cubed has got mass of 2.5 grams. So if we take the 140 how many centime cubes there are and times them by 2.5. So if we do the volume times the density we'll get the mass. So 140 * 140 * 2.5 is equal to 350 and that would be in grams. So that means the mass of the paper weight is 350 and that's it. So Siobhan's paper weight has got mass of 350 gram. Okay let's look at our next question. Question number 15. Okay so question number 15. Question number 15 says shown below is triangular prism. So, we've got this triangle or prism. It's got height of 14 cm, length of 20 cm, and we don't actually know which is the base of the triangle, and we're told the height of the triangle is 14 cm. Yep, the length of the prism is 20 cm. We're told the volume of the prism. So, we know the volume is equal to 1,232 cm cubed. And the question says, work out the length of the base of the triangle. So, we want to find So, we want to find here, the length of the base. Now, we've got the volume. Now, what I'm going to do here is remember to find the volume of triangle or prism like this, we would get the area of the cross-section. So, we' get the area of the triangle and then what we do is we times by the length of the prism to get the volume. So, if we work backwards and we take the volume and divide it by the length. So, if we take the volume and divide that by 20, the length of the prism, what that will tell us would be the area of this triangle. So, let's do 1,232 / 20. And that's equal to and that's equal to 61.6. So that means the area of that triangle will be 61.6 cm squared. So if you divide the volume by the length of the prism, you'll get the cross-sectional area. So we do 1,232 / 20, we get the area of this triangle. Now, this is fantastic. We've got the area of the triangle, the cross-section, which is 61.6. We know the height of the triangle, and we just need to find the length of the base of the triangle. There's few different ways we could do this. One approach is to work backwards because remember if we want to find the area for the triangle we do the base times the height and then half it and that's equal to 61.6. So if we take 61.6 and we work backwards so well let's double it. So let's times by two. So 61.6 * 2 is equal to 123.2. We now know what these two numbers times together to be. Then we can just divide it by 14. So if we do 123.2 2 / 14 that'll be equal to the base of the triangle. So we divide by 14 that's equal to 8.8. So 8.8. So that means the is equal to 8.8 cm. So we just worked backwards there. We knew the area for the triangle is found by doing the base times the height and then half it. So we took the area we doubled it and divided by the height and that gave us the base. So that was one approach. just want to change color of ink there to show you there's another approach that is obviously if we know that the area of triangle is half the base times the height. We can make little equation where we know the area of the triangle is 61.6 that's equal to half of the base times the height. So half time the base which is * the height which is equal to 14. And then you could solve this equation. There's few different ways you could solve this equation. You could get rid of the half by tsing both sides by two and then get rid of the 14 by dividing both sides by 14 and again you'll get is equal to 8.8. What probably would do is if was given this equation would do half * 14 which is 7. So get 61.6 is equal to 7 * and then divide both sides by 7 and again you'd get the is equal to 8.8. So that means the length of the base of the triangle is 8.8 cm. So that's it. So the length of the base of the triangle is 8.8 cm. Okay, let's have look at our next question. Question number 16. So, question number 16 says, "Shown below is solid triangular prism." So, we've got the solid triangular prism and the prism is made from titanium. So, this is solid titanium triangular prism. And we're told that the mass of the prism is 9.45 kg. So, that's how heavy it is. And we're told the density of the titanium is 4.5 per cime cubed. So, every single centime cubed of titanium has got mass of 4.5 And we've been asked to find the length of the prism. So we want to find the length of the prism. Okay. So what I'm going to do in this question is first of all I'm going to have look here the fact that the mass of the prism is 9.45 kg and I'm going to change that into grams to begin with because the density is in grams. I'm going to change the mass into grams as well. So there's th00and grams in kilogram. So we times this by th00and so that'll be 9,450 So that's the mass of the prism. Now if we know the density of the titanium that every single cm cubed has got mass of 4.5 If we divide the total mass by 4.5, that'll tell us how many centimeters cubed there'd be. So, in other words, the volume. If you divide the mass by the density, you get the volume. So, that means that the volume is equal to the mass divided by the density. If you divide 9,450 by 4.5, you'll see how many centimeters cubed there'd be. So, if we do 9,450 divided by 4.5, that's equal to 2,100. So that means the volume of this prism is 2,100 cm cubed. So that's fantastic. We now know the volume of the prism. We can then work out the area of the cross-section. So we can find the area of this triangle here. And once we find the area of this triangle, we can then work out the length of the prism. So let's do that. So let's find the area for the triangle. Remember the area of the triangle is equal to half the base times the height. So we're going to do half the base, which is 6 * 9, which is 54. Or you could do half of 12 * 9 and 12 * 9 is 108 and divided by 2 would be 54. So 54 cm squared. So that's the area of that triangle. 54 cm squared. Now this is fantastic because if we divide the volume by the cross-sectional area, we'll find the length. So let's do that. So let's do 2,100 / 54 and that tell us the length of this prism. So that's equal to would be equal to 2,100 / 54 is equal to 38.888 and so on cm. So that's fantastic. We've found the length of the prism. The length of the prism is 38.888 and so on centimeters. Or if we run that to two decimal places, that would be 38.89 cm to two decimal places. And that's it. So just to recap in this question, we divided the total mass. We changed the mass into grams. We divided it by the density to find the volume which was 2,100. We then found the cross-sectional area which was 54. And we divided the volume by the cross-sectional area and that gave us the length of the prism. And that's it. Okay, let's have look at our last question. Question number 17. So question number 17 says, shallow is swim that is full of water. So this swim's full of water and it's prism and the cross-section of the swim is trapezium. So you can see this cross-section here. And then we're told Cavon begins to empty the swimming pool at constant rate and the level of water goes down by 3 cm in the first 15 minutes. And the question says, how long does it take in total to empty the swimming pool? Okay, so to begin, the first thing we know is that the swimming pool is full of water at the very beginning. So it's full of water. So what I'm going to do is I'm going to actually work out the volume of the pool to begin with. So I'm going to find the area of this trapezium and then I'm going to times it by 14. So to find the area of the trapezium we do the area is equal to half of + * So that's the area of the trapezium. We've looked at that in previous questions. In terms of and that the two parallel sides that would be the 1.2 and the 2 here. So obviously if that's 2 that would be 2 So we've got and and is the distance between those two parallel lines. So if we look here that's equal to 25 So that means that that distance there would be 25 as well. So that means that the area of this trapezium would be half then in brackets plus So that would be 1.2 + 2. So 1.2 + 2 and then multiply by the distance between them which be 25. So now let's work this out. It's calculator question. So that's quite nice and that's equal to 40 squared. So the area of the cross-section is 40 square And then to find the volume of the pool we now need to times that cross-sectional area that 40 by the length of the prism which would be 14. So times by 14 and 40 * 14 is equal to 560. So 560 cubed. So that's the total volume of the swimming pool and we know that it's full of water to begin with. Okay. And then if we go down, we're then told that Kavon begins to empty the swimming pool at constant rate. So the water's coming out at constant rate and the level of water goes down by 3 cm in the first 15 minutes. So here obviously if we look at the swimming pool, the shallow end of the pool has got depth of 1.2 meters. The deep end of the pool has got depth of 2 meters. But in the first 15 minutes, the water only goes down by 3 centimeters. So it just comes down little bit. And actually if we consider that that would be cuboid because actually if it comes down going to sketch this in blue here. So what we' find is that level of water in the pool would decrease by 3 cm in the first 15 minutes. So if we actually work out how much water's left the pool. If we actually work out the volume of this cuboid, so the volume of the space in the pool above the level of the water, then that'll be how much water has left the pool. In terms of that cuboid, it would have length of 25 width of 14 and height of 0.03 because that's how much the level of water has decreased by in the pool. 0.3 which is 3 cm. So if we do 14 * 25 * 0.03, not three. That'll tell us the volume of water that's left the pool in the first 15 minutes. So let's do that. So let's work out the decrease. So that would be 25 * 14 * 0.03. And when we work that out, let's see what we get. So 25 * 14 * 0.03 is equal to 10.5. So 10.5 cubed of water has left the pool in the first 15 minutes. So that's fantastic. We now know the rate at which the water's leaving the pool. It's leaving it at rate of 15.5 cubed every 15 minutes. So, what I'm now going to do is I'm now going to divide that 10.5 cubed by 15 because that'll tell us how much water leaves the pool every single minute. So, let's do that. So, let's take 10.5 and divide that by 15. And that'll tell us how much water leaves the pool every minute. So, 10.5 / 15 is equal to 0.7. So 0.7 meters cubed of water leaves the pool each minute. So each minute. So that's fantastic because we now know how much water is in the pool to begin with. 560 cubed of water. We know how much is decreasing by each minute. 0.7 cubed. If we do 560 / 0.7, that'll tell us how many minutes it takes for the water to leave the pool. So 560. So 560 / 0.7 is equal to 800. So it would take 800 minutes. And actually if we go down to the answer section, it's actually got here hours and minutes. So we need to change 800 minutes into hours and minutes. So 13 hours 13 * 60 is equal to 780. So that would be 13 hours. So 13 hours is 780 minutes. And there'll be 20 minutes left over. So that'll be 13 hours and 20 minutes. And that's how long it would take for the water to empty the pool. So that's how long it take Cavon to empty the swimming pool. And that's it. And that's it. So these have been the video solutions to the corps practice questions on the volume of prism. If you need any extra help in finding the volume of prism, if you go to corps and go to the videos and worksheet section and go to video number 356. There's dedicated video tutorial there on finding the volume of prism. Alternatively, you can scan this QR code. But in this video, we focused on the video solutions to the practice questions. really hope you found this video useful. If you have found it useful, please like it and please subscribe to my YouTube channel. If you know anyone that needs any extra help with their maths, please also recommend Cor Mavs to them as well because it be really useful for them to hopefully use the resources as well. So, thanks very much and all the best. Cheers. Bye.