1 00:00:00,830 --> 00:00:06,470 Students in this video, let's discuss about the right circular cylinder. 2 00:00:06,850 --> 00:00:09,500 All right, now let's take an example. 3 00:00:09,680 --> 00:00:12,140 Over here, you have a right circular cylinder. 4 00:00:12,350 --> 00:00:14,790 Now, why is it called the right circular cylinder? 5 00:00:14,960 --> 00:00:17,270 You could have a cylinder like this also, right? 6 00:00:20,740 --> 00:00:29,260 Right over here, this axis is not perpendicular to this axis, right, but here you can see this is 7 00:00:29,260 --> 00:00:30,670 perpendicular to the base. 8 00:00:30,970 --> 00:00:34,890 So this type of a cylinder is what we call a right circular cylinder. 9 00:00:35,050 --> 00:00:37,360 And we only deal with this in this course. 10 00:00:37,360 --> 00:00:41,770 And even for your exam, you just need to learn about the right circular cylinder. 11 00:00:42,100 --> 00:00:42,490 All right. 12 00:00:42,640 --> 00:00:46,730 Now let's start to understand the surface area of the cylinder. 13 00:00:47,110 --> 00:00:52,930 Now, over here, imagine I'm cutting out this cylinder and opening it up like this. 14 00:00:53,290 --> 00:00:58,590 Now, let the height of the cylinder, be it and the radius of this part. 15 00:00:58,600 --> 00:00:58,810 Right. 16 00:00:58,890 --> 00:01:05,530 The circular part we are now, you can see that in this case, this will be X and this will be equal 17 00:01:05,530 --> 00:01:10,240 due to the right way to appear, because this is the circumference. 18 00:01:13,020 --> 00:01:18,770 Of this base, that's what we cut and spread out, right, therefore, this length will be to pay up 19 00:01:19,080 --> 00:01:20,370 and this will be it. 20 00:01:20,830 --> 00:01:27,570 Now we know how to find the area over here that would be too far into its right because this looks like 21 00:01:27,570 --> 00:01:28,470 a rectangle now. 22 00:01:28,590 --> 00:01:31,520 And we know area of a rectangle this length and breadth. 23 00:01:31,710 --> 00:01:35,490 Therefore, this area over here is to peer into it. 24 00:01:35,800 --> 00:01:36,230 All right. 25 00:01:36,390 --> 00:01:38,730 Now, what would be the area of this circular path? 26 00:01:38,880 --> 00:01:40,860 That would be Pyaar Square, right. 27 00:01:40,890 --> 00:01:43,440 We know that's the area of a circle. 28 00:01:43,680 --> 00:01:48,900 Now, having established this, let's note the lateral surface area of this. 29 00:01:48,900 --> 00:01:49,290 Right. 30 00:01:49,290 --> 00:01:57,090 Circular cylinder that would be to by our edge, which is what we got over here to the NSA of a right 31 00:01:57,090 --> 00:02:04,470 circular cylinder is to buy up its what about the TSA or total surface area that would be to Biarritz 32 00:02:04,470 --> 00:02:06,630 plus to Pyaar Square. 33 00:02:06,660 --> 00:02:07,010 Right. 34 00:02:08,260 --> 00:02:09,200 Why is that so? 35 00:02:09,400 --> 00:02:16,240 Because you have a circular area at the bottom and at the top, that's why you need to multiply by square 36 00:02:16,240 --> 00:02:19,460 with two and you add to that the lateral area. 37 00:02:19,480 --> 00:02:20,990 So this is the total surface area. 38 00:02:21,400 --> 00:02:21,800 All right. 39 00:02:21,940 --> 00:02:27,640 So we have learned how to find the natural surface area and the total surface area of a right circular 40 00:02:27,640 --> 00:02:28,150 cylinder. 41 00:02:28,450 --> 00:02:29,910 Let's move on now. 42 00:02:29,920 --> 00:02:30,460 Over here. 43 00:02:30,460 --> 00:02:34,300 We have our cylinder and this is radius R and this is height. 44 00:02:34,300 --> 00:02:36,820 It's now like a cuboid. 45 00:02:36,820 --> 00:02:43,470 You can see that the cylinder has a top and a base that are congruent and parallel to each other. 46 00:02:43,510 --> 00:02:43,800 Right. 47 00:02:44,050 --> 00:02:46,210 This double here and this base. 48 00:02:46,210 --> 00:02:47,400 Both are Sakalys. 49 00:02:47,620 --> 00:02:50,370 They are congruent and they are parallel to each other. 50 00:02:50,560 --> 00:02:57,070 Therefore, we can find the volume of this cylinder in the same way we found the volume of the cuboid 51 00:02:57,250 --> 00:03:01,420 that is volume is equal to the base of the area of the base. 52 00:03:01,660 --> 00:03:04,950 In the height of any of the base is Bayada Square. 53 00:03:05,140 --> 00:03:11,930 So volume over here is Spier Square into X, and that is the way you can find the volume of a cylinder. 54 00:03:12,100 --> 00:03:17,530 So we have seen how to find the large area, total surface area and volume of a cylinder. 55 00:03:17,800 --> 00:03:22,150 Now let's take a special case that is the case of a hollow cylinder. 56 00:03:22,360 --> 00:03:23,900 Now what is a hollow cylinder? 57 00:03:24,040 --> 00:03:25,180 It looks like this. 58 00:03:26,100 --> 00:03:28,240 Now, this is a rough sketch of a hollow cylinder. 59 00:03:28,440 --> 00:03:33,610 You can see that there is a space inside it which is hollow right over here. 60 00:03:33,630 --> 00:03:34,920 It's completely filled. 61 00:03:35,160 --> 00:03:40,620 But over here, you can see there is one more circle over here and anything inside this is hollow. 62 00:03:40,860 --> 00:03:43,500 So this is an example of a hollow cylinder. 63 00:03:43,650 --> 00:03:45,840 Imagine a pipe which is very thick. 64 00:03:45,840 --> 00:03:46,140 Right. 65 00:03:46,290 --> 00:03:47,840 So water can flow through it. 66 00:03:47,910 --> 00:03:49,860 So there is some hollow space inside. 67 00:03:50,040 --> 00:03:51,820 But imagine that it's very thick. 68 00:03:51,840 --> 00:03:54,510 So that would be an example of a hollow cylinder. 69 00:03:54,690 --> 00:04:02,040 Now, how do we find the volume of a hollow cylinder that would be piled into our square minus our square 70 00:04:02,190 --> 00:04:08,820 into its where capital R is this radius over here and smaller is this radius over here. 71 00:04:08,970 --> 00:04:10,590 Now, what is the logic behind this? 72 00:04:10,800 --> 00:04:18,690 This is the same as by our square inch, which is what we had over here, minus by our square inch. 73 00:04:18,990 --> 00:04:19,380 Right. 74 00:04:19,590 --> 00:04:23,600 So that's logical because this is the volume. 75 00:04:23,610 --> 00:04:28,780 If it was not hollow and we are just subtracting the part where it's hollow. 76 00:04:29,010 --> 00:04:34,290 So that is the volume that's to our square minus our square into a.