 Hello everyone, myself RC Biradar working as an Eastern Professor in WIT, in this video lecture we are going to learn about the development of the lateral surface of a right cylinder. At the end of this session students will be able to draw the lateral surface of a right cylinder. Introduction. Development. It is the plane figure of a 3D object we get after unrolling the 3D object on the development plane. So it can be done by using three different methods. First one is parallel line method, second one is radial line method, third one is triangulation method that is used for polyhedral. In first method cylinder and prisms will be done and here this figure is called a cylinder and this one is called as prism. A cylinder is having an external surface as curved surface and here we have imaginary lines on the cylinder surface called generators or elements. And we need to keep a cylinder on the development plane so that one element is on the development plane and we need to unroll the cylinder surface up to the last so that all the elements or generators are on the development plane and that will be the development of the lateral surface of a cylinder. In that figure we get all the elements are parallel to each other so it is called as parallel line method. And similarly for the prism also we get once we unroll all the vertical surfaces of prism on the development plane we get plane figure as rectangle having all the elements or vertical edges are parallel to each other. Second method radial line method it is used for cone and pyramid. So these imaginary lines on the curved surface of cone are called as generators or elements and the base of a cone is a circle, right circle and here we need to keep a cone on the development plane such that one element is on the development plane and after that we need to unroll the cone surface on the development plane so that all the elements or generators are on the development plane so that figure is called as development of the cone. Here if you see that one side of all the elements are having the vertex as their origin and this is the another end so these all the elements are radiating from the origin that is center. So that figure is called as the development of the cone and similarly we can have the development for pyramid also in the fashion. Third method triangulation method it is used for polyhedrons and wrapped surfaces. So for example triangular pyramid and tetrahedron and this method is used for the objects which are having triangular surfaces. In this figure we can see that a pentagonal prism is having two pentagonal surfaces one is at the top surface and another is at the bottom surface and since it is having five corners or five edges we connect this edge with this rectangle surface. So similarly we have five vertical surfaces and in this second figure if you see this so this edge is open means this vertical edge is cut so that all the five vertical surfaces can be arranged on a development plane so we get 2D object. So the length of this rectangle plane is equal to the five times the edge of the pentagon and the height of this line is equal to the height of the axis or height of the prism and these two pentagonal surface we get because two surfaces are there in one is in the top and in the bottom and this surface is called as a pentagonal prism development. Similarly for cylinder also in the second figure we get this figure here this generator is cut here so here we have two circles and if you unroll the curved surface of the cylinder on the development plane we get it as a rectangular surface of this line length equal to pi into D that is the circumference of the circle and the height of this rectangle is equal to the axis height or the cylinder height. So this plane is called as development of the cylinder full cylinder. So we take one example so in this example we are going to take a cylinder which is resting on HP with its base so we get the true shape of the circle on the top view that is on the HP plane. In the VP plane we get the front view of the cylinder so here the cylinder I have taken as a truncated cylinder truncated cylinder means it is cut using the cutting plane so here the cutting plane is inclined with HP at an angle of 45 degree with HP and the cutting plane is passing through the axis below the top surface by 25 mm that we are going to see the total height of the cylinder is 65 mm and that is equal to the axis height and without truncated if the cylinder is full we get this rectangle that is P A A P P rectangle for full cylinder and so we need to cut or divide this circle by 8 times any equal number of parts 8 or 12 so in the top view we get two circles here so both are coinciding each other one is for bottom surface and another is for the top surface so we need to name the bottom surface with P Q R S T U W and the top view and the top circle by A B C D up to H since the cylinder is truncated here so the front view looks like this and these lines are called as generators so these are projected from this top view points from A B C D E F G H and this can be projected here so here we get two generators two generators and this stretch out line must be divided by 8 parts because we have taken 8 number of divisions here and name them and connect this with the top points also when these are called as generators on the development plane and we get this point of intersection with a generator and the cutting plane so this here we get one two three four five here one more six seven eight so here we get two points because here we have two generators and here we have one generator so we have one point now to get the development of the truncated cylinder we need to transfer these points on these lines or generators so transfer these all eight points on this development so on the respective generator so first point is we get here and here also because this first point is on PA generator so in this PA is line here is here and one more PA line is here so we get this as point one similarly second point number two so here we get on generator Q B and point number eight on W H because both are on same height similarly three and seven four and six and five point we can project on this development plane and once we get all this point of intersection so connect these points with the curved profile because the cylinder is having the curved profile so once we cut we get the profile as curved so we need to connect all these points with the curved surface and this now this dark plane is called as development of the truncated cylinder now in this case I have taken cutting plane is inclined with HP by 45 degree now so this is the development plane we get so if we can think that if the cutting plane is inclined by 30 degree either we get the same profile of the truncated cylinder or what this is a reference plane I used thank you