Surface Area of Prisms and Cylinders Lesson 10 2

Hey guys, we're going to start notes 10.2 today, which involves surface area of prisms and cylinders. So the first thing that we're going to do is draw the nets of these shapes. Okay, the first two shapes we see here are both prisms. The first one is rectangular prism or square prism. If if these bases here are squares, right now this shape is sitting on its side. The bases are actually this rectangle here and this re rectangle here. They could be squares. Not sure. We're not given measurements. So, it's sitting on its side. And also, this shape here is also sitting on its side. The two bases are the two triangles. So this is triangular prism. So our first shape is rectangular prism. Our second shape is triangular prism. And our third shape obviously has two circular bases. This is cylinder. Okay. So, the nets for these guys, now forgive my drawing. I'm going to do the best that can. The nets for rectangular prism look something like this. Rectangular prisms have four rectangular faces and then rectangular two rectangular bases. So, when you fold all these up, it creates rectangular prism. triangular prism has three rectangular faces. Do the best can to draw this. And two triangular bases for total of five total faces. And cylinder has two circular bases and rectangle that folds up to make the lateral surface area, the distance around. Okay, so those are the nets of those shapes. let's go ahead and look at the actual formulas for lateral area and total surface area. Lateral surface area. So lateral surface area. Now surface area is just like if you were wrapping the outside of the box or the shape. It does not involve volume. It's all on the in it's not on the inside. It's all around the outside. So lateral surface area does not include the bases and the total surface area does include the bases. So the all these formulas are on your formula chart. the lateral surface area of rectangular prism. always call lateral surface area LA and it is big PH. Same thing with triangular prism. All prisms have the same formulas. So LA lateral surface area is equal to big PH. Well, what is big big just stands for the perimeter of the base. Okay. And the lateral surface area of cylinder, lateral surface area is equal to 2 pi rh. And all these formulas can be found on your orange or green formula charts that we have in class. the total surface area would include bases. So the lateral surface area plus the bases. So the total surface area or in other in other words that just the surface area is obviously the lateral surface area plus the area of the bases. So 2 * big Big stands for the area of the base. And since there are two bases with the prisms it will be 2 * Same thing for triangular prism. big pH, perimeter of the base, times its height, plus 2 * the area of its base. And the surface area of cylinder is the lateral surface area, 2 pi rhesi 2 because the area of circle is r² and we have two circles. So 2 r^ 2. Okay, with all this in mind, we're going to go ahead and look at couple problems. The first one, we're just going to start out nice and simple. This is rectangular prism. The shaded portion is its base. It's just sitting on its base. Find the lateral area and total surface area of the prism shown below. Use shaded face as your base. Okay, so first thing I'm going to do is I'm going to write my formulas. Lateral surface area of prism is big * the perimeter of the base time the height of the prism. The surface area is big perimeter of the base time the height of the prism plus 2 * the area of the bases. So before I'm going to do anything have to find the perimeter and the area of the base. Well, the base is the shaded region, which is rectangle. So, all we have to do is find one thing. First thing is the perimeter. So, obviously, I'm going to have to add up the sides of the perimeter. 8 + 6 + 8 + 6, which would be total of 28 And then the area of the base would just be length time width. 8 * 6 which would be 48. So with that information we have everything we need here to plug in. Now some of you might be wondering well what is this two for? This two is the height of your prism. So that would be your Okay so let's go ahead and plug this in. Lateral surface area is equal to the perimeter time the height of the prism. Well, the perimeter we found out was 28 * the height of the prism, which is 2. So, the lateral surface area is just 28 * 2, which is 56 squared. Okay, the nice thing about lateral surface area and total surface area is that total lateral surface area is always within the total surface area. For example, we already know what pH is because we found it over here. It's 56. So, perimeter time the height is 56 cuz we found it right here. Plus 2 * the area of the base. Well, we found the area of the base over here, which is 48. So, we have 56 + 2 * 48. Well, 2 * 48 is 96. So the total surface area is 56 + 96 which is 152 squared. Now it's still squared units because we're still talking about area. Surface area is form of area. It's the flat area around the shape. So 152 squared is our total surface area. Okay, we're going to continue on to example number two. Find the lateral area and total surface area of the cube below if each edge is five. Okay, so each edge is five. So all of the Oops, that's really bad line. All of these lines right here are five. Every single edge on here is five. Okay. so it really doesn't matter which one is our base because they're all the same. They're all squares. So, the first thing I'm going to do just to get it out of the way is to find the perimeter and the area of the base. Well, it doesn't matter which one we want to treat as our base, but we usually if there's shaded one, that's going to be our base. So, this is our shaded our shaded area. We're going to treat that as our base. So, the distance around our base would be our perimeter. 5 + 5 + 5 + 5 or 5 * 4, which is 20. And the area of our base would just be side time side or 5 * 5 which is 25. Okay, so we go back to our formulas. Lateral area and surface area the same as the previous problem in example one. Lateral area is big * Surface area is big * plus 2 big Okay, let's go ahead and continue with our lateral area. Lateral area is equal to our perimeter of our base, which we found was 20 times the height of our shape. Well, the height of our cube is still 5. So, our lateral area is 20 * 5, which is 100, and that's in centime squared. Okay. surface area. Again, the nice thing about total surface area, we already know the big pH if we found the lateral area. Big pH is just 100 plus 2 * big which is the area of the base. And the area of the base was 25. So, our total surface area is 100 plus 2 * 25, which is 50. And 100 + 50 is 150 cm squared. Very good. Okay, moving on to the back page. We're going to go ahead and save examples three, four, and five for class because they are extremely important and want to make sure we can all do them together. So 3, four, and five we're going to save for class. Number six we are going to do together right now. Number six is similar to number two that we just did because it's cube, but in this case, we are given the surface area. We're not given the edge or the side length. So, we're going to have to work backwards to find the edge of our cube. Okay. There's also couple of new formulas right over here. You're going to need to acknowledge. They are not on your formula chart, but will give them to you whenever you need to use them. like this question. So the surface area of cube is 1350. And it tells us right here that the total surface area of cube is 6 s^ squ. So I'm going to go ahead and plug in the fact that know that the surface area is 1350. I'm going to plug that in right here into our formula. So 1350 is equal to 6^2. So now I'm working backwards to find out what is So to get by itself, I'm going to have to first thing divide by six to both sides. So 1350 / 6 is just 225. And then when you have square squar and you want to undo square, we need to take the square root of both sides. the square root of 225 or what number times itself is 225? That would be 15. So the side length of our square, also known as an edge, an edge is the same thing as side length of of cube. I'm sorry, not square, cube, would be 15 in this case, 15 in. Okay. Now that we know that the edge or side length is 15 in of this cube, now we need to find the lateral area. And again it gave us the formula for lateral area of cube right here. Lateral area is equal to 4 s^2. So lateral area is equal to 4 * our side square which is the same thing as an edge. So 15 squared. We learned that from over here. 15 squared is the same thing as 225. So 15 4 * 15 squar which is 225 and 4 * 225 would be 900. So the lateral surface area of our cube is 900 in squared. Okay, we're going to go ahead and complete three, four, and five in class tomorrow. See you guys then.