 other working as an assistant professor in W. T. Solapur. In this video lecture, we will learn about development of the lateral surface of a right circular cone. At the end of this session, you will be able to draw the lateral surface of a right circular cone. So, this is a diagram, so how it looks as the cone. So, in this cone, basically cone is having a right circle as the base which is having a radius, a small r and it is having a axis height or cone height that is with a notation h and this yes is nothing but it is a true length of the generator or this is the outer surface of the cone is with this much length. So, this is the right circular cone 2D diagram and here in the 2D diagram from this. So, this is a dotted line we get because this curve or this part of the base circle is behind the solid object. So, we will not see this edge. So, we need to draw this with a dotted line and this is a 3D object of the first term of cone. So, here so this point is called as a vertex of the cone and here that vertex is cut. So, it is called as first term of cone and so to draw the development of the cone, we need to cut this cone at one of the generator. So, here we assume that there are n number of generators or elements on the periphery of the external surface of the cone and they are called as generators or elements. So, on any one element we need to cut this cone to make it as a 2D and once it is cut we need to unroll so that it is placed on the development plane. So, we get this type of 2D plane of the cone and if it is kept on the development plane we get a 2D object. So, let us see one example of a cone. So, here basically the cone is resting on the HP here. So and the cone is cut with the help of cutting plane or suction plane. So, which is inclined with HP at an angle of 45 degree and cone is passing through this point at this much distance below the apex point. So, this is a cutting plane inclination with HP and this 60 mm is the true length of this line. This is the true length of the generator. So, from apex to base circle that will connect. So, that is the true length that is 60 mm. Now so, since it is resting on HP so, from the top view we see that the base circle is on HP. So, that the top view will be a circle of 40 mm diameter and this point is apex point and here we will so, this is the axis height of the cone. So, this much length or this much height of the cone and this since O dash point we will not see from the top view. So, the axis will be seen it as a point in the top view and here we have cut this base circle by 12 points usually. So, to get the smooth profile we need to cut this base circle by 12 points. So, divide this 360 degree circle by 12 divisions. So, each will be of 30 degree each and name that intersection points 1, 2, 3, 4 and all. Now, here since this is the cutting plane angle with HP and these after this intersection we need to connect these points to the apex point. So, these are the generators or elements we call. So, these are basically the imaginary lines. Now so, this is a true length from 1 to 0 point is a true length of the generator or element it is of 60 mm length here. So, these are the generators we get. So, here we divide this circle by 1, 2, 3, 4, 5, 6, 7 and it is 8, 9, 10, 11 and 12 points we get. So, that will be reflecting here. So, usually so, that divisions are not showing here. So, please do not think that. So, there are no 12 divisions, but we have to divide this circle by 12 divisions and that points are reflecting over here. So, after cutting this cone by using the cutting plane. So, these generators are going to be intersect with the cutting plane this plane and we need to mark those points with a namings that is P1 to P12. So, usually that is the after 7 the points are not showing here, but there are 12 points actually. So, this is a point number 1, point number 2, point number 3 we get, point number 4, 5, 6 here and 7 here and again that 8 to 12 points are behind the cone. So, they are not seeing here, but there are 12 number of points. So, how to draw the development of the cone? Here, first of all we need to draw a fixer apex point here and from that point we need to draw one length. So, that is equal to the true length of the generator that is 60 mm. So, from O to 1. So, we need to draw 60 mm here we are going to cut the cone surface at generator O1. So, O1 will come in this left corner also and in the right side also. So, from this O1 to and this O1 line the degree that included angle will be be equal to that is equal to theta and that can be find using this formula that formula is R divided by L into 360 degree where R is the base circle radius. So, here it is 20 millimeter is a radius and length this capital L is the true length of the generator. So, that is 60 mm into 360 degree. So, we get theta as 120 degree. So, from this O1 to O1 we need to make an angle of 120 degree line or plane and from this point you connect this point with the help of compass. So, we get a curve line and divide this line by this circumference by 12 points or 120 degree divided by 12 will be 10 degree each. So, from that 12 10 degree each you draw these lines. So, this point will be as 2 and again 10 degree each. So, this point we get 3 4 5 up to 12 point we get. So, they are so like how so we need to get total 12 divisions on this curve line. So, now after that whatever the points we have marked here P1 to P12 that has to be transfer on this line. So, hence it is a true length if you say that this O1 and O7 seems to be 60 degree but not the O2, O3, O4, O5, O6. So, these lines are not with the 60 mm they are not the true length lines. So, what we need to do that we need to transfer this point number 2 3 4 5 6 and next 8 to 12 points should be transfer on any one of the true length generator that it may be on O1 O2 1 or O2 7 that has to be transfer. So, like how for example, so I will transfer the point number 2 on O1 generator. So, that will come on this O1 generator here. Similarly, point number 3 I will transfer by using the parallel projection on O1 line point number 4 on O1 line. So, we need to transfer all the points by using the parallel projection on to the O1 generator. So, that we get a point representative point of this P4 on this O1 generator with a true length because here all the lines O1 O2 O3 O4 O5 up to O12 are of with true length. So, to transfer this point of intersection, so we need to transfer these points on the true length line. So, that point we need to transfer here to get this profile. So, how to transfer these points? So, with help of compass so from apex point it so it will be easy to make it as easy. So, measure the distance of all the respective intersection points. So, from apex of the cone that is O2 O1 P1 O2 P1 and measure that distance with the help of compass and transfer that on this development plane. So, that distance should be transferred on O2 O1. So, we get this point P1 and similarly on this also we get this point as P1. So, similarly so whatever the point number 2 has been transferred on the O1 that point should be measure with help of compass and that point should be transfer here. So, we get this point as P2. Similarly, point number 3 measure from apex point and transfer it on O3 generator so that we get here. So, like all the points up to 12 points we need to transfer on true length line that is O1 and from apex point with the help of compass you measure that distance. So, transfer all the points on this respect to generators. So, after that connect all the points P1 to P12 with a smooth curve because here the cone surface the external surface of the cone is of a curve surface. So, once it is cut with the help of cutting plane we get a curve profile not the straight edge. So, since we get a curve profile so we need to transfer connect these points with a smooth curve or curve profile. So, join these points with a dark line and this dark line this also should be with a dark line and now this blue line surface indicating this as a development of the lateral surface of a cone like how we need to develop the cone or lateral surface. So, think that so what might be the profile if I change the direction of the cutting plane that is 45 degree instead of this direction this cutting plane 45 degree if I change that to this direction 45 degree or if this cutting plane is parallel to HP that is parallel to XY line what might be the profile whether we get the same profile or it might be with the slide changes think that and you can turn on the sheet this is the reference I used thank you