Engineering Graphics Class Module 4 _ IIT Bombay Professor _Semester 1 and 2 _ Episode 25
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00:00you
00:30This is our last section of this chapter.
00:39This is question number 13.
00:42Question 13 is a star question.
00:45These two questions are 30 and 31.
00:47Same question just the values are different.
00:50Both are important.
00:5130 and 31 and also 34.
00:54The speciality of the 13th question is that we are given a square prism with a base edge of 50 mm
01:05but the speciality is that the height of the prism is not given in the question
01:09So, the problem is of a square prism without a height
01:14So, the things are as follows
01:16The cutting plane is given
01:17The height of the square prism with a base edge of 50 mm is not given
01:20Then, it is cut by a plane
01:22Perpendicular to VP and Inclined to HP, the true shape is a hexagon
01:27So, we need a hexagon
01:29The speciality of the hexagon is that it is not an irregular hexagon but an irregular hexagon
01:34Because, it is given that the opposite sides are 25 mm and the remaining 4 sides are 35 mm
01:41Opposite sides are 25 mm and the remaining 4 sides are 35 mm
01:47So, we know that if it is a regular hexagon, the 6 sides will be equal
01:52Because, it is an irregular hexagon, the opposite sides are 25 mm and the remaining 4 sides are 35 mm
02:10If you are going to do it in that way,
02:12we cannot draw the simple portion fully
02:15So, why can we draw a base shape in this simple portion?
02:18Because, it is a square prism
02:19So, we can draw a square
02:21But, I have drawn the square in an equally inclined way
02:24The reason why I have drawn it in an equally inclined way is
02:27as I have said in the interaction video of the square prism and the cube
02:31If we draw it in an equally inclined way,
02:32we can easily cut the triangle, square, pentagon, hexagon, trapezoid and many other shapes from this solid
02:40I have done an interaction video on that
02:42You will understand when you see that
02:44That is why I have drawn it in an equally inclined way
02:46In the case of a square prism, if we want to get a hexagon,
02:49we have to place the solids in an equally inclined way
02:55That is why I have drawn it in that way
02:57Now, in this portion,
02:59I have told you that the true shape is a hexagon
03:02and the opposite sides are 25 mm and the remaining 4 sides are 35 mm
03:12Now, I have asked you to find out the height of this portion
03:15We cannot draw it without knowing the height
03:17But, what we have to do is
03:18we have to draw and find out the height of this portion
03:21How to do this?
03:23There is a particular method
03:24If you want to know the method to solve this problem,
03:28you can learn it by heart
03:30To know how to solve this problem,
03:33I have drawn two solids in a square prism
03:37You already know that
03:39If you want to get a hexagon,
03:41I have told you in the previous introduction video
03:43how to cut a hexagon
03:46To get a hexagon,
03:49Do you remember how to get a hexagon?
03:52To get a hexagon,
03:54we have to cut this line at the top and this line at the bottom
04:03If you cut those two lines and draw like this,
04:05you will get a hexagon
04:06If it is a regular hexagon,
04:08you have to cut this line at the top and this line at the bottom
04:15If you draw like this,
04:16you will get a regular hexagon
04:17Because,
04:18you will get two points if you cut this line
04:20and two points if you cut the middle line
04:22and two points if you cut this line
04:23I have told you that in the previous introduction video
04:25We don't have to draw the midpoint of this line
04:28Because, the true shape of our question is
04:31an irregular hexagon
04:32So, we have to cut this line at the top and this line at the bottom
04:38But, we don't have to cut the midpoint
04:40We can cut it any way we want
04:42But, what do we get when we cut it?
04:43Two sides should be 25mm
04:45and the other four sides should be 35mm
04:47to get a hexagon
04:49So, what I am going to do is
04:51I am going to draw an irregular hexagon
04:56I am going to draw an irregular hexagon
04:59I drew an irregular hexagon
05:02So, these two sides should be of opposite size
05:05That is 25mm
05:08and the remaining sides should be 35mm
05:10This is 35mm, this is 35mm, this is 35mm
05:13This is how we are going to get a hexagon
05:15So, this is how we are going to fix any edge
05:17If you draw a line in the middle
05:19Now, it is equal to half
05:21If you draw a line in the middle
05:23and if you take the edge like this
05:26We will not get any perpendicular V1 and V2 distances
05:29Is it clear?
05:31Now, suppose I take the edge like this
05:33For example, if I take the edge like this
05:36If I take the edge like this
05:38We will not know the value of this edge
05:40The perpendicular distance of this edge is
05:42This is our distance
05:43This point and this point are our distances
05:45So, we will not know the distance between these two distances
05:49So, we will know
05:51This is 25mm, this is 25mm
05:53and the remaining four sides should be 35mm
05:55So, I am going to take a hexagon in this
05:58Or, I am going to fix the edge in the middle
06:03Is it clear?
06:04So, that means
06:05If I draw a rough true shape in the problem
06:09I am going to take the edge
06:11Or, in this problem, I can take the edge
06:13Now, I am going to draw a rough hexagon
06:28This is an irregular hexagon
06:30I am fixing these two opposite sides
06:33Opposite sides are 25mm
06:35This is 25mm
06:36This is 25mm
06:37I am fixing
06:38The remaining four sides are 35mm
06:40So, I am going to take the edge in this
06:42Like this
06:43We can make the hexagon equal half
06:45If I take the line in the middle as an edge
06:47We will not know the value of that
06:49But, when we fix the vertical distances perpendicular to that
06:53The first vertical distance is
06:55This is our vertical distance
06:57V1
06:58That is equal to 25
07:00The next vertical distance is
07:02V2
07:04We don't know the value of that
07:06The next vertical distance is
07:08V3
07:09We will get the value of that
07:10V3 is equal to 25
07:12So, we have V1 and V3
07:14We will get two vertical distances
07:16If we fix the edge horizontally
07:20We will get the vertical distance
07:22So, I am going to solve the problem in that way
07:24So, if I fix it like that
07:26In the same way, I have fixed the vertical distance and horizontal distance
07:29So, now we have to know
07:31Where do we normally fix the vertical distance?
07:33This is where we are going to fix the vertical distance
07:35Now, I know V1 is equal to 25
07:37So, what did I do?
07:38I fixed V1 at the point where 25 comes
07:42I got 25
07:43So, we will get these two points
07:45Usually, we project these two points straight up
07:49We have to start from where it comes
07:51So, we got the starting point
07:54Now, we just have to cut this line down
07:56But, we cannot cut it anywhere
07:58Next, I am going to fix V2
08:00So, V2 is equal to 25
08:02I fixed V2 at 25
08:04So, if we fix V2 at 25, we can project it down
08:06So, we will get this point
08:08What can we do?
08:10We can draw a section plane like this
08:12So, what do we get?
08:14We have V1 and V2
08:16The remaining four sides
08:18We can draw a vertical line with a chance of 35
08:22But, there is a problem
08:24This is a rough sketch
08:26I have already drawn the height here
08:28But, there is no height
08:30So, we know one thing
08:32If there was a height
08:34The distance from this point to this point
08:36was h
08:38This is the actual h
08:40If we know the value of h
08:42We can solve the problem
08:44I have not drawn the height here
08:46Is it clear?
08:48I am not drawing the height
08:51I have not drawn the horizontal line
08:53We don't know where it will extend
08:55So, I have not drawn this
08:57The center axis line was also extended
08:59I don't know how high it will extend
09:01The center line was also extended
09:03We don't know where this will extend
09:05But, we can know one thing
09:07What was the vertical distance?
09:09It was 25
09:11So, I have fixed the first vertical distance as 25
09:13So, I have fixed the first vertical distance as 25
09:15Then, I have drawn the 25 line
09:17I drew the line of 25 straight up.
09:20Because I don't know how far it will go.
09:21I drew it straight up because there was a height here.
09:25If there is no height, what can we do?
09:27We can just draw it straight up.
09:30So I don't know how far it will go.
09:31Next I fixed V2.
09:3425
09:35No, V3. 25.
09:37But we can extend that.
09:39Because we can extend that to the base.
09:40The base is already there.
09:42So I got that.
09:43So I got this point.
09:45I don't know the point on top.
09:47If you look at this side, you will know.
09:48I got this point.
09:49I don't know the point on top.
09:50There is this line.
09:52What can we do to get the point on top?
09:54From here, if we know H,
09:57if we draw an arc from H to the composite,
09:59we will get this top point.
10:01Right?
10:02So what I am doing is,
10:02if we know the value of H from this point,
10:04I am repeating, if we know the value of H,
10:08from this point,
10:09take H as the composite.
10:11Then this red line,
10:12if I take H and cut it to the line where 25 was fixed earlier,
10:16I am drawing H.
10:17So this is the value of H.
10:18If we know H,
10:20if we cut it,
10:21what will that be?
10:22The top point of this solid.
10:25Because we can fix it there.
10:26So what can we do?
10:27We can close this solid there.
10:28This is this much.
10:29So we can determine the height of the solid.
10:33So this is the height of the solid.
10:36The height of the solid is H.
10:37Is it clear?
10:38So even if we have the value of H,
10:40we can find the height of the solid.
10:43So in the problem that we fixed here,
10:46in this problem,
10:46the value of H that we took,
10:49the value from here to here,
10:51we don't actually know the value of H.
10:52What we know is V1 and V3 only, 25.
10:57So if we can find the value of H,
10:59even if we draw a true shape,
11:02we can complete this solid.
11:07We can complete it.
11:08So for that,
11:09to find the value of H,
11:12what we are going to do is,
11:13we are actually going to draw a true shape.
11:15So in the actual case,
11:16how do we draw a true shape?
11:19So to draw that,
11:20if you look here,
11:22I have already drawn the axis in the middle of this square.
11:26You can see how I am going to draw a real true shape.
11:31So I extended this axis line horizontally.
11:36Then there is the bottom corner of this.
11:38I am going to extend the bottom corner line horizontally.
11:49So I extended the bottom corner line horizontally.
11:54So this is the bottom corner line.
11:56Then the top line.
11:58I extended the axis line in the middle,
12:01this line and this line.
12:03These are the three extremes of this solid.
12:04These are the three extremes in the middle.
12:06So I extended those three lines first.
12:09Now we know where to fix the vertical distance.
12:12The first vertical distance V1.
12:14I am going to scale it perpendicularly.
12:16How much should it be?
12:18How much should it be?
12:19It is 25.
12:20So 25.
12:23Let's see where it should be.
12:33So V1 is 25.
12:35I am going to fix it.
12:381, 2, 25.
12:45So I fixed V1 at 25.
12:49So this is the distance V1.
12:51I fixed 25.
12:54Similarly, we can fix V3 at the other side.
12:57It will be at the same height as V3.
12:59So there is no problem.
12:59If you fix V1 and draw a horizontal line, what will you get?
13:03If you mark here, you can fix it quickly.
13:06If you scale it, you can fix it quickly.
13:11So if I measure it from here, how much is it?
13:15Around 25.
13:18There is a dimensional error.
13:201, 2, 25.
13:28Okay, keep it correct when you draw.
13:30So V1, V3, 25.
13:32So these distances are 25.
13:34I fixed both of them at 25.
13:36Next, I am going to extend the projector lines that I fixed at 25.
13:43So when you first fix it, you have to take the correct dimension to get the correct height.
13:47I have not done it so accurately.
13:50You can do it accurately.
14:06Okay, I am going to project those lines at 25.
14:16These are the projector lines at 25.
14:19Next is this.
14:22This is the first line I drew.
14:2425 will be a little less.
14:26So I drew the projector line at 25.
14:28So it is the same.
14:29Here also 25.
14:30So here I am taking 25.
14:31I am taking V3 at 25.
14:32I projected those two lines.
14:35This is the middle line.
14:37This is the line projected at the top.
14:39This is the line projected at the bottom.
14:41When we fixed V1, V3, we got two points.
14:45So these are the lines projected at those points.
14:48So we projected the points and drew them.
14:51Now we are going to fix it.
14:53Here we are going to draw the real true shape.
14:56We already know that this is 25.
14:59I fixed the first base edge at 25.
15:04This is the first base edge of our hexagon.
15:07I fixed it at 25.
15:09Now we are going to take the compass to get the next 4, 35.
15:13We already know that we have to get this when we cut this.
15:16So these are the two extreme lines.
15:18So how much do we take in the compass?
15:2035 is the remaining 4 sides.
15:22I am measuring 35.
15:24I am measuring 35.
15:26From this line which we got 25,
15:29we are going to the extreme end which we drew at the top.