Problem 8.5 Development of Surfaces of Solids – A hexagonal prism with 40 mm sides of its base is resting on H.P. and two sides of its base are perpendicular with V.P. It is cut as per the figure given below. Develop the lateral surface of the hexagonal prism.

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**Procedure:**

**Procedure:**

* Step-1* Draw a horizontal x-y line of some suitable length.

* Step-2* Draw a hexagon of side of base 40 mm below the x-y line at some suitable distance from it, such that two of the sides of the hexagon should be perpendicular with the x-y line as shown in the figure. Give notations on it. It is top view of the Hexagonal prism.

* Step-3* From the center of the hexagon in the top view, draw a vertical center line of length 60 mm from the x-y line as shown in the figure. And from the all notations of the hexagon draw vertical projectors of length 60 mm from the x-y line as shown in the figure. It is a rectangular shape. And Give the notations on it. It is front view of the hexagon.

* Step-4* Draw the shape as per the dimensions given in the figure with medium dark lines and medium dark smooth circle.

* Step-5* Draw a line from the top of the hexagon in the front view exactly parallel with the x-y line, and make a vertical line between the x-y line and the line drawn from the top of the hexagonal prism at some suitable distance from the line d’-4’, as shown in the figure. And give the notations 1-A on it as per the figure given above. From the point A, divide the x-y line in the 6 divisions in such a way that the distance between two consecutive divisions should be equal to the length of a side of the base of the hexagonal prism, which is 40 mm.

* Step-6* Then give the notations on it in capital letters like, A-1, B-2, C-3, etc. as shown in the figure, connects these all the points with light straight lines, these are the vertical edges of the hexagonal prism. It is a rectangle. And it is the development of the vertical surface of the hexagonal prism.

* Step-7* Now transfer the distances of all other points from the front view in the development of the hexagonal prism at appropriate places, which can be known by the notations of the vertical edges, as shown in the prism. Then connects these points in sequence by medium dark straight lines or medium dark smooth curve and make the boundary and the vertical edges of the development of the hexagonal prism as dark lines as shown in the figure.

* Step-8* This is the development of the vertical surface of the hexagonal prism.

* Step-9* Give the dimensions by any one method of dimensions and give the notations as shown into the figure.