 working as an assistant professor in W. T. Solapur. In this video lecture, we are going to learn about the development of the lateral surface of a pentagonal prism. At the end of this video session, students will be able to draw the lateral surface of a various regular prisms like square prism, pentagonal, hexagonal prisms. So, this is a question. So, it is a pentagonal prism with edges of the base 25 mm and axis 65 mm rests on one of its base edges with an edge of the base parallel to and nearer to the VP. It is cut by a suction plane perpendicular to the VP which is inclined at 30 degree to the HP and which is passing through the top end of the axis. A cylindrical plane of radius 30 mm and perpendicular to the VP cuts the prism and the origin of that passes through the right bottom corner of the cylinder, sorry prism. Draw the development of the lateral surface of the prism. So, for proceeding the answer. So, first of all, we need to draw the x-y line. Name it as x-y line. Next, we need to draw the pentagonal surface with one of its bases parallel to VP. If it is parallel to VP, so one of the edge of the pentagonal surface will be parallel to x-y. So, I have drawn one edge parallel to VP or x-y. So, the second line of the pentagonal surface. So, it is having an external angle between two lines is 72 degree 72 degree. The third line, fourth line and fifth line. So, this is a regular pentagonal surface which is having external angle 72 degree each. And after that, so name this with a A B C D E. So, this is representing a bottom pentagonal surface. So, because here the pentagonal prism is having two regular pentagonal surfaces arranged. So, which are parallel to each other and they are apart a distance of that is equal to the axis height or that we can call it as a height of the prism. So, in the top view, we see that two pentagonal surfaces are coinciding with each other. So, the bottom surface is naming with the A B C D E and the top surface is with the P Q R S T. Next from this we need to draw the projection to draw the front view. So, these all are the projections we need to draw to draw the front view. And now this line is indicating the vertical edge of the pentagonal prism that the name is 80 and it is having 65 mm the length of axis also. Next in the line CR we are drawn. Next we need to draw the top surface that is a P Q R S T surface. Next connect the DS vertical edge. Next these two will be drawn with the dotted line because AP line and B Q vertical edge we cannot see from the front view. So, we need to draw this with the dotted line application. Next name these bottom surface and the top surface with their namings like A B C D E bottom surface and P Q R S T top surface. Next thing is that so after this the prism is full prism here. So, for the full prism the development is we get as a rectangular surface of a stretch out line equal to 5 times the edges of the pentagonal surface that is 25 into 5 we need to draw 125 mm line. Next 65 mm height line that is indicating the height of the prism and the bottom surface and the top surface again with the 125 mm and connect the corners. So, this becomes a development of the full prism. Next name these with a A B C D E here I have divided the 125 mm stretch out line by 5 times because we have 5 corners in the pentagonal surface. So, we need to divide this 125 mm line by 5 times and name those with a A B C D E bottom surface. Next connect this intermediate points from bottom surface to the top surface with a vertical edges and name those as P Q R S T. Next thing is that so we need to cut a prism by using two sectional paints or cutting planes. So, here one plane is 30 degree with HP and this is passing at the what we can say top corner of the axis and which is 30 degree with HP and one more cutting plane is a curve plane which is the center of that is passing through the right bottom corner. So, which is having a 30 mm radius. So, this looks like this after using two section planes. Next thing is that we need to draw the projections from those intersection point between the section planes and the point of intersection with the bottom edge at the bottom surface. So, these are the intermediate projections I am going to draw to get the intermediate points. So, now here I have written the point number A on line ED or DE. So, next is B C D E F G and H. So, these are the intermediate points I have drawn or I have written to draw the intermediate points in the development plane also. So, next thing is that we need to name the intersection point between the vertical edges and the sectional plane that is curved section plane. So, the first point is coming on line ED. Next thing is that point number 2 is coming on line B. The point 3 is on DS, point number 4, point number 5, point number 6, 7, 8, 9, 10, 11. So, these are the intermediate points we need to mark to transfer these points on the development plane. We need to clearly observe that so, where the points will be coming and why there are two points I have marked and why here only one mark. So, since here we have only one vertical edge. So, the section plane is intersecting it only once. So, we need to mark it as one only one point. So, here 5 and 7 is because of here D vertical edge and H vertical edge. So, it is intersecting twice. So, we need to mark with two points. So, similarly here also C and one more is that BQ vertical edge. So, it is intersecting two vertical edges. So, I need to mark with two points. So, similarly here up to this. Next thing is that we need to mark these points also on EDH that is 12th point, 13th point is on DS, 14th point again it is on G vertical edge and 15th point is on AP vertical edge. The next thing is that we need to transfer these intermediate points on the edges of the pentagonal surface. So, we need to transfer those points here between these respective edges. So, that we can done by transferring the distance from any reference point. So, like how we can transfer. So, after that we need to transfer or we need to connect these points from bottom surface to the top surface. So, these are called as a vertical edges from those respective points. So, next thing is that we need to draw the parallel projections to get the points in the development plane. So, that we can done by drawing the parallel projection. So, here I have drawn the parallel projection from 2 and 10 point. If we see that the point number 2 is coming on the vertical edge B and point number 10 is coming on vertical edge F. So, this point this projection is up to this vertical edge B. So, we cannot transfer this up to A because. So, this projection is only up to this B A and in the next stage draw the parallel projection from 3 and 9 point. So, since the point number 3 is on a vertical edge that is a ds if you see this. So, we need to transfer this line up to this ds vertical edge in the development plane and the point number 9 is coming on this vertical edge that is 9. So, the next is that we need to draw the projection from 4 and 8. So, that is coming on C vertical edge and the point number 8 is coming on vertical edge BQ. So, like how we need to transfer all the projections from all the respective point of intersections. So, here we get the point of intersection between these vertical edges and the projections drawn from this respective points. So, next thing is that we need to write the names that is with a 1 to L1. These are the point of intersections on this vertical edge. So, write those with 1 2 here 3 4 5 6 up to L1. So, next thing is that we need to connect these what point of intersection with a profile that is smooth profile that is curve profile. So, since we need to draw this with a curve profile because if you see that the curve profile is intersecting the parallel this plane profile. So, we get a curve profile as the profile here. So, that connect this with a curve line. So, this 1 2 12 and 6 to L1 this is the profile after cutting with a curve profile. Next thing is that we need to transfer this point number 12, point number 13, 14 and 15. So, point number 12 is up to this ET because the point number 12 is coming on ET vertical edge. Next is that 15 is coming on PA since this point is on PA vertical edge. So, next name those point of intersection with a naming 12, 13, 14 and here 15. So, we need to connect these 14 and 15 with a straight line because if you see that this section pin is also a plane surface and it is intersecting a plane surface. So, we get a straight edge as a profile. So, this is also point number 15 here because since we have one more PLN here. So, connect this 12 and 15 with a straight line and 12 and 13 straight line and 13 and 14 with a straight line. If you see that so, this profile is the development of the truncated prism and after this we need to increase the thickness of the line. So, to indicate that as a development surface of the prism. So, like how we need to dark the the external lines after cutting. So, this plane is a final front to after section or cutting and this dark surface indicating the development of the prism after cutting. So, you can think that so, this is a profile I get if this section plane is 30 degree with a HP what is that the change we can get in the profile if the section plane is 45 degree instead of 30 degree or this point is passing through this point or whether the profile is same or we get some modification in the development plane. These are reference I used. Thank you.