1
00:00:00,610 --> 00:00:07,780
I students, welcome to the section where we deal with solids, now we start with identifying the volume

2
00:00:07,780 --> 00:00:08,650
of a cuboid.

3
00:00:08,980 --> 00:00:09,400
All right.

4
00:00:09,550 --> 00:00:14,320
Now, before we get to a cuboid, let's think of what we mean about volume.

5
00:00:14,650 --> 00:00:19,750
Volume is the amount of space occupied by a three dimensional object.

6
00:00:19,960 --> 00:00:20,370
All right.

7
00:00:20,590 --> 00:00:22,750
Now, over here we have a cube, right?

8
00:00:23,020 --> 00:00:27,910
So over here, the length, breadth and height all is equal to one centimeter.

9
00:00:28,120 --> 00:00:34,330
And this space, this amount of space is what we define as one centimetre cube.

10
00:00:34,540 --> 00:00:38,920
That is one centimeter into one centimeter into one centimeter.

11
00:00:39,160 --> 00:00:39,610
All right.

12
00:00:39,730 --> 00:00:42,490
Now, over here, I have a cuboid right now.

13
00:00:42,490 --> 00:00:46,870
You can see that in this cuboid, eight cubes are included.

14
00:00:46,870 --> 00:00:47,110
Right.

15
00:00:47,320 --> 00:00:49,140
So you have included aid groups.

16
00:00:49,150 --> 00:00:52,470
That is one, two, three, four, five, six, seven, eight.

17
00:00:52,750 --> 00:00:59,200
Therefore, the volume of this cube out over here has to be eight times the volume of this cube.

18
00:00:59,200 --> 00:00:59,540
Right.

19
00:00:59,680 --> 00:01:04,360
So that is equal to eight to one, which gives you eight centimetre cube.

20
00:01:05,380 --> 00:01:08,080
All right, now, let's keep this aside.

21
00:01:09,140 --> 00:01:15,920
Let's try to find out how we can find the volume of any cuboid now over here, because we kept four

22
00:01:15,920 --> 00:01:22,640
cubes side by side, the length has become four centimeter, the bread is just one centimeter.

23
00:01:22,820 --> 00:01:26,150
And you can see that the height over here is one plus one.

24
00:01:26,150 --> 00:01:29,150
That's two centimeters right now.

25
00:01:29,270 --> 00:01:35,600
You can see that the volume, which is what we got over here, can be found by multiplying four, two

26
00:01:35,600 --> 00:01:36,170
and one.

27
00:01:36,290 --> 00:01:40,250
So volume is four in the two in the one that's equal to eight centimeters.

28
00:01:40,400 --> 00:01:42,860
And that's the same value that we got over here.

29
00:01:43,190 --> 00:01:46,040
Now you can see that over here to find the volume.

30
00:01:46,040 --> 00:01:51,980
What we have done is we have found the area of the base that's four into one and then multiply it with

31
00:01:51,980 --> 00:01:52,430
the height.

32
00:01:52,710 --> 00:01:56,300
So volume is equal to area of the base into height.

33
00:01:56,520 --> 00:02:04,610
Now, this can be used for any shape where the base and the top, where the bottom and the top are congruent.

34
00:02:04,610 --> 00:02:04,970
Right.

35
00:02:05,340 --> 00:02:09,920
For example, will see that the same is applicable in the case of a cylinder.

36
00:02:09,920 --> 00:02:16,010
Also over here, in the case of a cylinder, you can see that the bottom and the top are congruent and

37
00:02:16,010 --> 00:02:16,730
it has a height.

38
00:02:17,060 --> 00:02:22,700
So over here also, you can apply this formula that is the volume would be area of the base into the

39
00:02:22,700 --> 00:02:23,000
height.

40
00:02:23,460 --> 00:02:30,410
Now let's proceed with Cuboid and quickly revise what we have learned and also learn some more interesting

41
00:02:30,410 --> 00:02:31,070
properties.

42
00:02:31,320 --> 00:02:35,860
But over here we have a cuboid of Langdell, Brett B and Height Edge.

43
00:02:36,140 --> 00:02:42,550
Now, over here you can see this shape has six faces, twelve edges and eight.

44
00:02:42,560 --> 00:02:43,660
What is this now?

45
00:02:43,670 --> 00:02:44,720
What are the faces?

46
00:02:44,930 --> 00:02:51,260
For example, this is one face similar to this over here is one face and this is the third face.

47
00:02:51,440 --> 00:02:53,720
Now you can see that there are three more faces, right?

48
00:02:53,720 --> 00:02:57,680
You have one over here, one at the bottom and one behind this one.

49
00:02:57,920 --> 00:03:00,410
But there are a total of six faces now.

50
00:03:00,410 --> 00:03:02,210
It just are these sites.

51
00:03:02,240 --> 00:03:04,880
OK, so there is one, two, three, four.

52
00:03:05,000 --> 00:03:06,350
That's Force A just.

53
00:03:06,620 --> 00:03:11,630
And then on the back side, also, you will have four, the four plus four and over here you have one

54
00:03:11,820 --> 00:03:13,430
and this is another one that's two.

55
00:03:13,640 --> 00:03:16,810
And similarly over here also you have one and over here you can have one more.

56
00:03:17,120 --> 00:03:19,670
So that's four plus four plus two plus two.

57
00:03:19,670 --> 00:03:21,160
That's equal to twelve edges.

58
00:03:21,350 --> 00:03:22,610
And what about what it says?

59
00:03:22,760 --> 00:03:24,300
It has eight vertices.

60
00:03:24,500 --> 00:03:26,490
So what is this are the corners.

61
00:03:26,510 --> 00:03:29,300
So that's one, two, three and four.

62
00:03:29,450 --> 00:03:31,390
And you'll have four on this side also.

63
00:03:31,400 --> 00:03:32,360
That's four plus four.

64
00:03:32,510 --> 00:03:33,800
It's equal to eight.

65
00:03:33,830 --> 00:03:34,490
What is this?

66
00:03:34,760 --> 00:03:35,200
All right.

67
00:03:35,390 --> 00:03:40,270
What about the lateral surface area of the keyboard and what is the lateral surface area?

68
00:03:40,400 --> 00:03:46,000
It's the area that let me clean this up and show you what we mean with the natural surface area.

69
00:03:46,250 --> 00:03:53,510
It's this area or here, this one plus this one plus the side opposite to this and the side opposite

70
00:03:53,510 --> 00:03:53,990
to this.

71
00:03:53,990 --> 00:03:54,350
Right.

72
00:03:54,620 --> 00:03:58,640
So the little surface area is equal to two times this area.

73
00:03:58,880 --> 00:04:01,160
Let's do the last two times this area.

74
00:04:01,160 --> 00:04:09,140
So that is equal to two times into it for this one and two times B Interreg for this one little area

75
00:04:09,140 --> 00:04:13,100
is equal to two times Elitch plus two times, be it.

76
00:04:13,700 --> 00:04:15,950
Now what about the total surface area?

77
00:04:16,070 --> 00:04:22,370
To find the total surface area, you need to add the top area and the bottom area to the lateral surface

78
00:04:22,370 --> 00:04:22,790
area.

79
00:04:23,180 --> 00:04:30,950
So the total surface area is equal to two times L, B plus B plus L, right.

80
00:04:31,400 --> 00:04:33,260
l.B gives you the bottom and top.

81
00:04:33,260 --> 00:04:36,500
Right, two times B, which is this and this side.

82
00:04:36,710 --> 00:04:41,720
And then you have Elitch, which is this side and the one in the other side of it.

83
00:04:42,020 --> 00:04:44,030
Now that's the total surface area.

84
00:04:44,420 --> 00:04:45,840
We call it DRC.

85
00:04:46,190 --> 00:04:47,900
Now what about the volume?

86
00:04:47,900 --> 00:04:50,840
We have seen that the volume is in the bread into height.

87
00:04:51,020 --> 00:04:51,370
Right.

88
00:04:51,560 --> 00:04:57,890
And the last property that we learn over here is that the length of the body diagonal is root of L squared,

89
00:04:57,890 --> 00:04:59,760
plus B squared, plus eight square.

90
00:04:59,900 --> 00:05:01,230
Now, what is a body diagonal?

91
00:05:01,510 --> 00:05:02,900
Let me clean this up a bit.

92
00:05:03,800 --> 00:05:10,260
The body diagonal would be the line segment joining this point over here with this point over here.

93
00:05:10,880 --> 00:05:16,090
So it is the largest line segment that you can put inside that quote.

94
00:05:16,310 --> 00:05:20,780
And that would be root of L squared, plus B squared, plus eight square right now.

95
00:05:20,790 --> 00:05:21,310
Why is that?

96
00:05:21,320 --> 00:05:25,560
So let's dig in lower here and be over here.

97
00:05:25,850 --> 00:05:30,500
Now, this diagonal would be root of L squared plus B squared.

98
00:05:30,500 --> 00:05:31,970
Right, ASPO Pythagoras's theorem.

99
00:05:32,180 --> 00:05:33,800
Now let's add it to it.

100
00:05:33,910 --> 00:05:39,890
It is also perpendicular if you take this one, this is the body diagonal that would be a square root

101
00:05:39,890 --> 00:05:41,060
of it.

102
00:05:41,060 --> 00:05:45,820
Squared plus square off root and squared plus B square.

103
00:05:46,370 --> 00:05:52,610
Right when you square root of L Square please B square you will get just L squared plus B square and

104
00:05:52,610 --> 00:05:54,130
you have it square also over here.

105
00:05:54,410 --> 00:05:59,960
Therefore the length of the body diagonal of a cuboid will be root of L squared plus B squared plus

106
00:05:59,960 --> 00:06:00,530
it's square.