 Hello everyone, this is Shila Ratna Banswade from Walshan Institute of Technology, Solapur. Today we are going to see the topic sections of solids and in that particular we will be seeing the cone type of solid. Let us move further, learning outcome, students will be able to draw the sectional view of cone. Now cone is a solid of revolution where when we rotate a right angle triangle by the side adjacent to 90 degrees we get a cone. Cone does not have faces rather it have generators and no edges. Generators are imaginary. It has a base and a point at a top called as apex. Let us move further with an example. A cone base 60 mm diameter and axis 70 mm stands vertically with its base on HP. The section plane perpendicular to VP and parallel to one of the end generators of the cone passes at a distance of 15 mm from it. Draw the sectional plan and the true shape of the section. I suggest you to pause the video and recollect the position of the cone. Now moving further as mentioned the cone stands vertically with its base on HP. We can recognize from this that the cone is stationed or is resting on HP with its base as it stands vertically. The same cone is cut by a plane or a section plane perpendicular to VP and parallel to one of the end generators. Let us consider the first condition perpendicular to VP that means the plane or the cutting plane will be seen as a line view in the front view plus it has to be parallel to one of the end generators of the cone and it passes at a distance of 15 mm from it. The cutting plane should be 15 mm from the end generators. For this we need to draw the section plan that is the sectional top view and the true shape of the section. Let us start by drawing first the XY line or the reference line. Now as the cone is resting on HP on its base let us start with the top view by making a circle at this position that is below XY with the base diameter of 60 mm. So draw a circle of 60 mm as the cone will be seen in circular fashion in top view. This is the 60 mm diameter base of the cone. Now further divide this circle into equal number of parts. For this instance we have divided the circle into 8 number of parts. You can divide this into 12 or even more number of parts. Let us move further for drawing the front view we will project each and every point in the front view like point 1 is projected vertically upwards, point 2 and 8 being on the same line, point 3 and 7 on the same line, point 4 and 6 on the same line and point 5 in the vertically upward direction. So this forms the base of your cone in front view. Let us complete the cone. So this is the cone with height 70 mm in front view. Now let us join the generators. So these are the generators of the cone. We will name them as 1 will be named as 1 dash. Similarly 2 and 3 and 4 into 2 dash, 3 dash, 4 dash and so on. Now you can see this apex 2 1 dash is 1 generator, apex 2 2 dash, apex 2 2 8, 2 8 dash is another generators and so on. Now the cutting plane is parallel to either this 1 dash generator or 5 dash generators because for this condition the end generators and this particular view are O2 1 dash and O2 5 dash. So our cutting plane will be parallel either to this or this. Now let us move for drawing the cutting plane or section plane. So this is the section plane. For this current video we have taken this parallel to O1 dash. You can also take this cutting plane parallel to OF dash. It should be 15 mm from O1 dash. So this is the cutting plane which cuts the cone which is resting on HB. Now further mark the points where the cutting plane cuts the generators or the base. For example here the cutting plane when cuts the base 1 dash 5 dash we have named it as P12 because base being in circular fashion we get 2 points. Moving further at the middle generators it cut at point 3 and 4 P3 P4. Base generator 5 and 6 and at the end only one generator cuts so we have named it as P7. So here you can see in the top view at this point you get the base at 2 points similarly the middle generators this point and this point similarly this generator one over here and at the end only single point. Now let us project each and every point from the front view or the cutting point from the front view in the top view. So projection of P12 will be on the base that is point this and this similarly projection of point this 4 and 5 sorry 5 and 6 and 3 and 4 will be over here. So point 4 and 6 cuts O4 and O6 similarly point P7 cuts generator O5. Now the point which is at the middle generator or the axis of the cone we need to project that point in front view as this lies on the same line we cannot directly project it for that we need to do a construction project this P34 either on O1 dash or O5 dash. Let us project this I have projected it on O5 dash further I will project it down so we will get P34 over here now these points actually belong to generators 3 and 7 so let us project this backwards on 3 and 4 so encompass take distance OP34 in the front view and rotate this point towards O7 and O3 in this fashion so that you will get the points P3 and P4. So these are the corresponding points that you get on the generators now by joining all these points you will get the required sectional view of the cone. So this area is nothing but your desired sectional top view of the cone the remaining portion of the cone is darkened and this part is removed. Now let us move further for true shape of the section. Now for true shape of the section we will draw the section line parallel to XY on this point on this line let us mark the point P12, P34, P56 and P7 with the help of a divider or a compass. Project these points vertically downwards like P12 will be projected vertically downwards and the corresponding point P1 from the previous top view and P2 from the previous top view. You will get the points P1 and P2 similarly we will project the remaining points and we will get the points as you can see on the screen. Let us join these points. So as you can see this area is the required true shape of the section when a plane is cut when a cone is cut by the given plane with the given condition. So this gives you the true shape of the cut section of the cone. Thank you.