## Problem 8.4 Development of Surfaces of Solids – A hexagonal prism is resting on H.P. on its base with two edges/sides of base parallel to V.P. One equilateral triangular shape of size 20 mm is cut from the prism such that the axis of the triangle is perpendicular to V.P. & parallel to H.P. & passing through the center of the height & width of the prism. Develop the surface of the prism. Take side of base 30 mm and height of axis 80 mm of the prism.

**Procedure: **

**Procedure:**

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

* Step-2* Draw a hexagon of side of base 30 mm below the x-y line at some suitable distance from it, such that two of the sides of the hexagon should be parallel 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 80 mm from the x-y line as shown in the figure. And from the all notations of the hexagon draw vertical projectors of length 80 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 cylinder.

* Step-4* Draw an equilateral triangle of length 20 mm in the middle of the length and height of the front view of the hexagonal prism in such a way that the center of the triangle should be at the distance 40 mm either from the bottom or the top of the front view of the hexagonal prism as shown in the prism.

* 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 cylinder 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 30 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 the sides of the triangle 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 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.